Only if (! Here comes the beginning of long list of assumptions again. I'll keep it short, and not unravel the tangle of different "ifs") you try to put the same scene in the smaller frame the way you did in a larger format's frame.
And even then...
DOF is a computed distance range of acceptable sharpness based on focal length, aperture, subject distance, and the value for acceptable circle of confusion for a given format. The "acceptable" part is somewhat subjective, but the typical values used to compute DOF tables and scales are based on things like typical enlargement factors and viewing distances for the format and the average limits of human vision. There is no way to calculate DOF without making those assumptions.
It is also perfectly reasonable to deviate from those assumptions, based on one's personal standards for sharpness or planned enlargement factor. In other words, you may decide that you are planning to make a big print, so the value used as the acceptable circle of confusion should be smaller in that particular case. Most people don't actually make that computation, but just stop down one or two stops from the aperture recommended by the DOF scale on the lens or DOF table, which is the result you would get by computing the DOF with a smaller than typical value for acceptable circle of confusion for that format.
You may also decide to stop down for other reasons, like reducing falloff of illumination with a wide lens or reducing spherical aberration or field curvature, since DOF isn't the only component of sharpness.
Manufacturers make the depth of field scale based on the size of the circle of confusion. If I recall correctly, Leica uses 0.003". The D.O.F. scale is a only guide, not a true indication for all possible uses of the camera and film.
If you consider the blur caused by the shallow D.O.F. to be a flaw, of course it will be magnified as you enlarge the negative to a bigger print size. Someone else may consider that same effect a bonus [search for "bokeh"].
There's an article on depth of field on Wikipedia.
If you find, by experience, that the depth of field guide gives negatives [and therefore prints at the end-size] with too shallow D.O.F., take appropriate measures to remedy that [stop down]. If setting the focus by hyperfocal technique, use one stop smaller to increase depth of field to your liking. Suppose exposing at f/5.6. Use the near/far marks for f/8 instead. Or even f/11.
Again, the D.O.F. scale is only a convenient guide that will satisfy most [not all] users. It is not a universal cure-all.
Regardless, it is a fine point that doesn't significantly affect the rest of what I said.
In most cases a standard is arbitrary, even though it may be objective. For example, a licensing body may decide that a passing grade on a professional certification exam is 70%. That is an arbitrary choice. (Why not 72%?) However, it is an objective criteria. In other words, once the standard is determined one does not have to subjectively discuss whether a score of, say 69% is a passing score.
Choices for standards are almost always arbitrary. For example, a definition of optical resolution based on the Rayleigh criterion is arbitrary. However, it is objective because two different people can perform the measurement and come up with the same result without having to apply subjective judgment.
Similarly, choices in definitions of depth of field that I discussed above may be arbitrary, such as the choice of a standard viewing distance. However, they are objective in the sense that they can be unambiguously measured.
I do know what 'objective' and 'objectivity' are supposed to mean.
So that's not it.
Just take one of your arbitrary choices: "perceptible by a person".
Who would that be?
The DOF criteria were set using large panels of people, with the criterion they ended up 'defining' being some sort of statistical mean.
No other way. No 'objective', or even common, thingy in sight.
"The most important thing about DOF, by far, is that it is a perceptual thing. Not an 'autonomous' entity with an absolute dimension. (Despite all the formulae and calculators people like to let loose on it)."
A viewing distance may be measured 'objectively'.
But so that 'arbitrary choice' may be 'objective' (we can set up a thread about whether 'objective' is a meaningful concept at all. But another time perhaps ;)).
But we're not concerned about viewing distances, but with how an image looks (!) from that viewing distance.
Totally and utterly not objective.
The definitions of DOF and CoC are well known, and anybody can look them up. Simple simple.
For DoF scales DoF gets smaller as the format gets smaller.
In this case you're assuming constant distances while varying FoV/enlargement. So a smaller format has LESS DoF due to what you're keeping constant. Put another way, you're projecting exactly the same image, but cropping it and enlarging it more. So your CoC has to go down, and so does your DoF. For "equivalent image" comparisons the change in distance more than counteracts this, but that's not the comparison you want for DoF scales.
And the dpreview guy's crack about the scales being useless for APS because they're calculated for FF is especially idiotic. Just shoot a stop or so down from the line you're reading on the lens. Duh.
Getting back to the more useful "equivalent image" case, it may just be f-stop and magnification, but for different fields of view you can only match the magnification at a single plane. So with, say, a 15 vs. a 500 (assuming same format), if you keep the subject plane magnification the same (by changing distance), the magnifications some distance ahead of or behind it will be different. For short DoF this is trivial, but stop down enough at non-macro distances and there will be a large difference in DoF.
And I really don't see the point in arguing over the standard DoF definition. Yeah, yeah, it's right about as often as a stopped watch. But they needed some sort of standard, this is at least a marked-on-the-lens starting point to correct from to get to appropriate numbers for your 16 x 20 enlargements or 4x5 contacts or whatever else it is you're doing that isn't a mediocre 8x10.
If we assume we are dealing with one frame size only, frame size drops out of the equation as a constant, and field of view is a function of focal length and distance only.
Focal length and distance combined are magnification.
Now it is not true that DOF on film changes with field of view. When magnification and f-stop are constant, DOF will be too, no matter how large or small the frame.
Frame size enters the equation when you want to compare different frame sizes. ;)
Let's keep the distance constant (for simplicity's sake). Then you need a shorter lens to fill a smaller frame the same way you fill a larger frame with a longer lens. That means magnification is smaller, DOF larger on the smaller format film.
When you want to compare same size images, from the same viewing distance (or smaller images from a shorter viewing distance, such that the apparent size is the same), magnification will be the same again, and so will DOF (there are a few side effects that will change the apparent DOF, but i'll ignore those for now).
Or (in short): the field of view is unimportant. Any difference you see when changing frame size is that in frame size.
There will not (!) be a large difference in DOF at all.
The thing that is correct is that unsharpness, the fore- and background blur, increases more rapidly when longer lenses are used. So there is a visible effect of focal length.
But that is outside the DOF. DOF itself is still the same, as long as magnification and f-stop are the same.