I have been an on and off yoga practitioner for about 20 years, but am not an expert in any way, I am nothing close to regular.
From what I have read some postures are contraindicated for TOS - anything with your arms over your head can be rough. Downward dog can be rough. So unfortunately it would be hard to teach those postures if you rely on examples. That said I don't know anything about yoga instructor training and whether you would need to do everything like that. You would be very sensitive to people with contraindications though and that would be a great attribute in a yoga instructor in my opinion.
However, I have read that some postures are excellent for TOS and my guess is that it would depend on you personally. I have been able to do some light home practicing of some postures and they definitely help me. If nothing else, they relax me which helps with everything. I find twists to be great as they mobilize my back and neck. Of course one has to warm up into a twist...
I also found this article which I refer back to often. Postures such as bridge or anything that opens up your chest without putting the wrong kind of strain on your arm are really good.

Unfortunately I don't have enough posts to paste a link so go to the Yoga Journal website and search for "Have you gone numb". It is a great article.