Booker and Kyrie can absolutely co-exist as a back court, but they are gonna be woefully awful on defense. Booker needs the ball in his hands, but he's also an excellent shooter/scorer. The problem is Booker and Kyrie both like to score, and take the last shot. So it really does come down to whether or not you firmly believe Booker is willing to commit to defense.
A better trade would be Jaylen Brown+ T-Roz, and 2 first round picks.
Allows Smart to PG/SG as a sixth man, and allows Booker to have free space on the floor during the 1st and 2nd unit to ball handle.
I also forget Booker is only 21, and while his team isn't that good. He's already putting up similar numbers to Kyrie, and is only 0.2 APG behind Kyrie's.