Lots of great info so far guys!

The movements DECREASE depth of field. They change the location of the plane, but a tilted plane winds up with less depth front to back than the plane parallel to the film.
Ok this confuses me, I was under the impression that using movements you could basically bring everything from the near limit to infinity into focus with the caveat that you are losing focus area in the foreground above the focal plane (and I suppose also below it depending on whether or not the extended plane of focus intersects with the ground). In other words, compared to a system that isn't utilizing a tilt, you end up with much less front-to-back depth near the camera but an enormous amount more at great distances from the camera. Is my thinking still wonky here?

No matter what you do, if you are using a LF camera for street work, the heisenberg uncertainty principle (and hence Schrodinger's cat) apply. You cannot take a picture without your subject knowing that you have a camera. Get used to that idea.
Ha! I like the analogy. I tend to shift between modes of discreet shooting and very overt shooting, I've gotten called every name in the book by now so in general I don't have a problem being noticed by the subject and will adopt whatever shooting style the camera allows for. I guess I should have specified this from the beginning; I'm interested in shooting from a tripod with a studio camera as I do all my hand held with my mamiya MF. My general strategy will be to choose a location, compose, and wait for something or someone(s) interesting to happen. I tend to think though, that while the view camera will have a much more noticeable presence than an SLR, the act of shooting will be much less overt and that subjects, overall, will be less aware that they are being photographed.