The players can individually do whatever they want. They're independent contractors; the ATP isn't a union that makes binding choices for all its members. The ATP is merely the players' group that organizes the professional tour.
The main problem is that if players banded together to destroy a tournament, they could face charges for breaking antitrust laws. Moreover, the top players are risking creating a schism in men's pro tennis by threatening this boycott; they won't really help the struggling players by breaking away and making the early rounds of ATP events less compelling than they already are.
So realistically, the chances of an AO boycott are zero.