Go is actually a finite two-person game of perfect information and cannot end in a draw. Then by Zermelo's theorem, it is exactly one of the two has winning strategy, either Black or White.
So my question is which one? the Black or the White?
Update: Despite of the game is too large to calculate directly, my (roughly) idea is to prove inductively, from 3x3, 4x4 until 19x19. If for any $n$, one player(suppose black) has winning strategy, then it seems a conclusion that the player(black) has winning strategy.
Update: It seems the result is also rely on the scoring rule.
So another idea is to consider scoring rules, since the more compensation the White earned, the higher probability the winning strategy White has. Different results may be yielded within area scoring and territory scoring.