I would say its a 50/50 as to who pays for it. I would want to pay for the survey myself just so there is no question as to who the suveryer is working for. I would also try to use a local (to the boat) surveyer that was recomended by an independent source, such as someone on this board.
I just missed a deal on a Florida boat and my plan was this.
1) Send a deposit check contingent on securing insurance and the survey. (Insurance was quoted and accepted, just needed the binder)
2) Have the survey lined up for the day I arived in Florida.
3) Sea trial the boat and have a local dealer go through the motors.
4) Through a wire transfer have my bank pay off the loan on the boat, directly.
5) Write a check, wire transfer or pay cash for the balance do to the current owner.
6) Trailer the boat home.
I figured, with a bit of advanced planning, this could all be done in 1-1 1/2 days.
The surveyer and engine shop were recommended by board members here that were in the same area as the boat I was looking at.