Well... yes, in that it was a major third party, and as such had more success than most in getting candidates elected. But if you're asking whether or not it continues to have an impact on politics to this day, I doubt it.

Probably their most lasting impact is the shift of the impression of Freemasonry which was partly a result of the Morgan Affair itself (the event that kicked off the Anti-Masonic party), partly the Anti-Masonic Party's doing and in part the loosely related wave of anti-Masonic rhetoric of that era.