I suggest you test it for yourself. It's really the only way to know for sure since there are so many variables. As I said before, the conventional wisdom regarding staining developers (of course this is a generalization as there are many different formulas) is that to get maximum imagewise stain, it is best to keep the process alkaline or neutral from start to finish, and to keep sulfite low from start to finish. This would mean use a water stop instead of acid stop bath, and use a neutral or alkaline fixer with low sulfite (example TF3 with sulfite removed or TF4). Although Gerald presents valid arguments to the contrary, the chemistry of film processing always appears to be somewhat more complex than expected. It is also important to keep the words "maximum stain" in perspective. It's easy to come away from certain readings with the impression you will get hugely different amounts of stain depending on whether or not there is sulfite in your fixer, or whether or not you use an acid stop bath/fixer. The differences are likely much smaller than that, which would tend to support Gerald's reasoning.

The degree to which the after-development alkaline and low sulfite requirements are true is likely somewhat variable depending on the formulation, development technique and the film. The only way to know for sure is to try. The one piece of conventional Pyro wisdom I would say is least true is the recommendation to put the film back in the developer (ie alkaline environment) to increase stain. Everything I've ever read on the subject indicates all this will do if anything is increase general stain (ie fog), not imgewise stain.

Just to show different Pyro formulas work differently, one notable exception to the conventional rules is Wimberly's WD2H+. Wimberly is one of the founding fathers of modern Pyro developers. Regarding WD2H+ (a developer that produces an fairly strong orange-yellow stain), he makes a point of indicating this developer's stain is achieved entirely in the development stage, and is made permanent at that stage, so that there is absolutely no difference in the final negative whether you use an acid stop bath, and acid fixer, versus a neutral or alkaline after-development process.

Testing 510-Pyro and your film with different fixers would be relatively easy. Expose and develop two negatives identically, fix one in an alkaline fix (with sulfite), fix the second negative in Ilford Rapid Fix. Bleach away the silver and see if one negative has more stain. If you see no difference you could then do a sulfite test. Try giving one of the negatives a standard hypo clearing agent treatment and see if there is a loss of stain.