I don't see any reason to go to that effort. The problem for me is that I wouldn't want that solvent to get into places where it can hide and prevent your fresh oil from doing its job. If there's goop and stuff on the ring and pinion I would just wipe it off with a rag and call it good.
On the other hand, some folks would check gear backlash, runout, and all that good stuff, so in that case yes I suppose you need to do a pretty thorough cleaning. Just depends on how much work you want to do.