How Bleach & Oxi-Clean Affect Vulcanite Stems

Not sure, but I have never used bleach on my stems. The oxiclean will do the trick without any worry. Then take a magic eraser to it (I use the cheap generic brand) and then you can't go wrong with a quick wet sand with very fine sandpaper, your oil of choice and your golden.
I know your asking about bleach though but I thought I would tell you my routine. I'm sure someone will chime in though.

I think, what is never considered with these treatments, is that the inside of the stem will look just as rough, as the outside. While this would not affect looks, I am afraid, it will affect smokability, as the rough surface will collect more moisture, than a smooth one, but nobody I know is polishing the smoke channel after such a treatment.
My take to this is, that I use tooth paste and elbow grease to clean the outside of stems. I would put nothing on them, what I would not also put in my mouth. Generally I leave the smoke channel as is, but if I sense a bad sulphuric taste to the smoke, I put tooth paste on a pipe cleaner, insert it into the stem, attach a drill and let it rotate for a minute or so. Just check, that the stem does not get too warm. Then I check with a LED lamp, if the smoke channel is smooth, and if not, I repeat the treatment.

Before any interior cleaning goes on I take Simple Green and spray the pipe and stem down and scrub the exterior with an old toothbrush. Then the pipe sits overnight before I take the steps mentioned below. (Don't forget before and after pictures.)
I have used bleach 1:12 ratio for 20 minutes, and it worked fine. I've also used Oxyclean and Everclear - Oxy for 30 minutes and scrub with an old toothbrush, then scrub the interior with Everclear soaked pipecleaners until clean. Then I turn the mouthpiece down in a small glass and soak it in Everclear for 20 minutes. Either way will sterilize the stem & mouthpiece - then you're ready to start polishing.
Don't forget the pipe shank when you're cleaning the bowl. I use pipecleaners and vodka with Qtips until it's clean, then a salt and Everclear soak for the bowl. When I'm done, the pipe is shiny and happy.

I am using Colgate Total Advanced Whitening. Something in there just seems to take the green stuff right off, but others might just work the same or better.

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.

I use the heat method, I find it's the quickest and doesn't require any sanding after.

Boil a small pot of water on the stove ,add a heaping teaspoon of baking soda and soak stem for about five minutes . Clean while still warm with paper towels . Polish with tooth paste and then cover with Chap Stick and let it soak in for a day or so .Clean off excess Chap Stick .Not perfect but it works .The flame from a candle will also pull the gunk to the top as Andrew suggested .