I can't imagine it differently. The advantage of the first move is in my opinion an advantage for white, yet too small to force a win. The GM's are very good at chess. If chess would imply a win for white, then would imho the rate of won games at the GM level be much higher then currently is.
Hasn't there been research indicating that the higher the rating of both players is, the bigger the chance that the game ends in a draw?
No not for me, for all the games I played in USCF, 60% of them ended in draws
I would definitely agree to challenging you to a match whereas the condition would be I'm white the whole way.
What say you?