For anyone that plays nba 2k14 on ps4, is there any way I can play with the new rookies from this draft on the rosters? Say in a quick game.

I'm not sure if you can in quick games. But if you go into MyGM mode it allows you to download custom made draft classes from other people then when the season ends you can draft the players.

I'm not sure if there's a way to add them to your roster for other game modes though.

This. In quick match, press triangle. All you have to do is find someone who uploaded a custom 2014 draft