Vulcanite stems become discolored because of oxidation. The oxidation products (probably sulfur oxides?) lead to the bitter taste that one gets with heavily oxidized vulcanite.
Caveat: I'm not a restorer. I've cleaned a few stems on my own pipes but I'm far from an expert on pipe restoration. Many have worked out a process that works for them and I don't wish to start a battle with those who have restored hundreds of pipes and always do it a certain way.
With that out of the way, bleach and oxy-clean are oxidizing agents, which means that they will further oxidize the vulcanite -- both outside and inside the stem. It will do this very quickly. Yes, very long term exposure of vulcanite to bleach or oxy-clean will ruin the vulcanite. I would not expect that the short soak that folks use on their stems will do significant damage to the stem, aside form oxidizing more and requiring the removal of more stem material.
As an aside, many think that bleach or oxy-clean clean things really well because they remove stains and because bleach kills bacteria. Stain removal is primarily by oxidation of the offending stain. Color depends quite a lot on chemical structure and when you oxidize whatever has color, you change the structure and it is no longer colored. The byproducts of the oxidation may, or may not, be removed, but the color disappears so your shirt looks clean.
Some say that soaking in bleach or oxy-clean makes the oxide layer easier to remove. I don't have enough experience to say. What I can tell you is that there is more oxidized vulcanite to remove after soaking in bleach or oxy-clean. Because of this, I don't use either. On an oxidized stem (again, only a few) I just start with the magic eraser and stick to mild abrasives. I don't quite see the point in creating a thicker oxidized layer and subsequently sanding off more of the stem material. But, if it really does make it softer, it might be a good trade off?
Yes, the inside of the stem will be oxidized by the bleach or oxy-clean. The bleach or oxy-clean do not know the difference between the inside and outside of the stem. I have no idea if it affects how the pipe smokes. It seems that enough restorers use, or have used, bleach or oxy-clean with good results that it is does not cause problems.
Rinsed well, and it should be rinsed well because you are going to put the stem in your mouth, I doubt that there is any long term damage from the bleach or oxy-clean. I certainly would not recommend a bleach treatment a few times a year, because you will be sanding off a lot of material after the treatment, but a few times in the lifetime of a pipe is probably no big deal.