Likely yes, because win-date (i.e. total turns played) has a substantial effect on score: the fewer turns to the win, the higher the game-score will be — and the
whole point of AP is to reduce the number of turns needed to finish a (multiplayer!

) game. But it would not surprise me in the least to learn that when the Firaxis devs added multiplayer, they forgot to adjust the scoring-algorithm to account for using AP (after all, they certainly didn't add an adjustment-factor to the base-turns for Worker-jobs).
But map-size and victory condition will
also affect victory-date.
For any given victory-condition, games on Tiny/Small maps tend to be won earlier than on Standard, simply because there is proportionately less land to cover/ conquer, and research-rates tend to increase earlier due to that, plus the lower map-size factor (which is applied to the base tech-costs).
Similarly, Domination wins can (easily) occur in the Medieval/ early Industrial (using MWarriors, Gallic Swords, or Knights, Cavs and UU-equivalents), whereas a Diplo-victory will be very difficult for the human player to achieve before they reach the Modern Age — because it's necessary to build/capture the UN (if an AI owns the UN, it won't hold a vote that it "knows" it's going to lose),
and have the resources/ cash/ techs/ diplomatic relations to encourage the remaining AIs to vote for you, rather than The Other Guy (Diplo-
losses can occur before you go Modern, though!).