I have been attending a Toastmasters regularly for approximately six months and, having never tried any form of therapy or treatment, I can say that it does help to the extent of your effort.
You're never pressured to speak if you're not comfortable, nor give speeches regularly; you are encouraged to initiate your own goals, roles, and speeches whenever you feel like it. If you don't want to do speeches, you can take on smaller, dedicated roles like Speech Timer or Speech Evaluator, which only require maybe 2-3 minutes of speaking. Doing those usually gives me enough buzz for the day haha.
Or skip all that and just do Table Topics, which is fun once you get a handle on how to answer a question. Like someone else had said above, if you have nothing to say about a certain topic just go with the first thing on your mind. It's a very free-flowing exercise and great practice for when you feel like you have nothing to say or contribute.
The other members are very supportive and speak only positively and constructively of your performance. As someone with SA, recognize that going up to the podium is an achievement in itself. Know that other members only want to see you succeed, and only through more critique and more practice will you grow out of habits.
I've only completed one speech so far, but I've taken a number of other roles and participated in every single Table Topics so far, and I can manage to see a slight change in my ability to think on my feet. It's not world-changing but small steps are better than leaps, at least for me. I've also begun chatting with a regular member after our meetings so that's left me with some optimism too.
With that said, I would like to see more Toastmasters activities that involve more than one person. If you are looking for a chance to practice social dynamics, then Toastmasters may be too formal a setup. I'm currently looking into free Advanced ESL classes to help develop my social skills.