I am doing it, and have been for than 5 years. Most of it was low dose, but full transitioning dose now. I've not had any problems passing as male, although I'm careful to hide my breasts and have a stubble instead of clean shaven - I don't look normal if I shave.
I changed to full HRT as I couldn't stand it anymore, and perhaps that will happen again and I'll transition socially as well. I'm fighting myself not transitioning, and I've discovered that can cause serious problems. I have fear about social transition, but it not my main motivation (or I hope not).
You can always try it and see how it goes. I don't think there's any reason not to, as many people don't present female immediately anyway. You might not be able to stop there, but I guess that's when you overcome the fear and finish it.
I certainly believe its possible to get a therapist to sign off on it, perhaps depending on where you are and who you'd see. I didn't even try so I can't say for sure.
If I were to do it again and seek approval, I must admit I'd be tempted to lie and tell the usual story. I don't have any moral issues doing that, and they wouldn't find out for a really long time anyway and by then its not really important. The real problem is if you actually need the therapist for therapy, and not just to sign the paperwork. Lying is going to compromise what you get out of therapy, and with the fear you have you probably need it.