After the first pair of moves, an abort with no record of the game is no longer possible.
From that point until White makes his/her 4th move, the game will be recorded and a win, loss or draw awarded but no ratings adjustments will be made to either side.
Once White has played the 4th move, the game - if rated - will result in ratings adjustments depending on outcome and the players' statistics.
I just played a couple of bullet games where my opponent resigned after the 2nd and 3rd move respectively as he dropped a pawn in one and did not like the opening in the second. The ratings did not change. I thought that a game is on once the first pair of moves has been exchanged. Are there different rules for bullet games?