No. No one is going to know how long it will take. I believe getting a Visa is up to the country. I know that when I was in the MTC, there were some missionaries who were delayed to their country because of Visa problems. On my mission, I had to go to the border of the country each month to renew my Visa.
So, unfortunately, you won't be able to put a timeline on the Visa. You may get people telling you of their experience, but don't count on it being the same for you.
Good luck, Elder, to you and your brothers.
I say that we need to teach our people to find their answers in the scriptures...But the unfortunate thing is that so many of us are not reading the scriptures. We do not know what is in them, and therefore we speculate about things that we ought to have found in the scriptures themselves. I think that therein is one of our biggest dangers of today."
--President Harold B. Lee, December, 1972