Big league bullpens are full of guys who failed as starters who became closers. Just off the top of my head of Sox / ex-Sox guys, I can think of ReyLo, Hendriks, Jenks, Colome.
Kopech has shown he can't be counted on to be a starter. He's got talent (read: "stuff"), and it seems like he'd be able to be an effective bullpen arm.