It appears that SEGA has announced that free to play MMO Phantasy Star Online 2 will be coming to PS4, at least in Japan. The game is currently available on PC and Vita, though a dedicated western release has yet to happen. A release for North America was announced a few years ago though that never came to be. The website for that release is still up but remains unfinished.
If we’re going to go by that evidence then it is likely North American and European PS4 owners won’t get a chance to play Phantasy Star Online 2.