Quick Hook Question

If I set my sub 1M LH & RH specialists to also serve as closers vs L/R respectively, does the quick hook designation also apply to them like it would for the specialist roles?

Don't think I've ever seen anything that makes a differentiation between those two roles, so I'm just seeking clarification and any ideas or information is appreciated!

quick hook/slow hook, if set, applies to any pitcher when he enters a game. The reason he got into game makes no difference--the only exception is if you are out of pitchers/relievers for some reason (a long extra inning game for instance)