From what I have heard now it seems that it has two effects in VFS - it makes the voice better for some months during recovery, so you can after the 1-2 months of voice rest sound good again and people will not say that you got worse. It gives a good voice, a good feeling and enables a normal interaction in daily life. As it wears off this effect has to be kept up with medication and then later with voice exercises until hopefully no additional intervention is needed? The other effect seems to be that using the voice while it is not in a relaxed state early on, it can damage the voice. My voice doctor explained to me that generally if there is hypertension or assymetry occuring and the voice is too forced, the vocal folds will "smash together" instead of gently touching. So I gues this is also why botox is given, so you dont tend to do this sort of thing. Apparently I did this in the past and the solution was to do voice rehab but with VFS you need to wait for some months until you can do that, so that is probably why they bridge that gap with botox and medication.
Thats how I think about it at least.
Amy got away without Botox. Her way to get this was to concentrate on really doing clear and nice sounds during the voice examination to avoid jitter and vibrato or "vocal tremor". If you can make a very clean sound, I think they can skip Botox as it means you can use your voice in a soft way that does not do any damage. I can imagine to have good voice training before that focussed on relaxation and also to have some sort of singing experience might help. My voice analyst told me last week that I have an excellent low jitter and voice health index now, so I guess I would have some chance there

Oh and I think Jenny or Sarah was told to get regular Botox injections later on, but I dont think they went ahead with it and it still seems good.