FYI there are some problems with your plan (in case you haven't already guessed). First of them is that RA employees are not easy to rehire under any circumstances. Not only must your service record be marked as "re-hireable" by your current manager, but whoever is thinking of rehiring you must get approval from several levels of their own management chain, along with the legal and HR departments. This pretty much eliminates the possibility of being rehired within the same division, and the same issues exist even if you apply for employment in another division.
With that said...if you were to get rehired after your exit date (as distant a possibility as that may be), then you'll keep your severance...you did leave the company, after all. On the other hand, if you get "rehired" before your exit date, then HR treats you as if you just switched departments. There was no separation, and no termination of employment, so you get no severance.