A Playstation fan asked Sony boss Shuhei Yoshida if local co-op will work between remote play on a Playstation Vita and a Dualshock 4, all on the same console:

https://twitter.com/jeedee/status/394190759093878785

Shu responded:

@jeedee if the game has same couch coop, it will

— Shuhei Yoshida (@yosp) October 26, 2013

So there you have it, remote play with the Playstation Vita will be as seamless as another controller when it comes to couch co-op.