It's not quite as bad as "incompatibility". This post has a response from Buckman Labs that make PolyQuat indicating that though chlorine breaks down PolyQuat into shorter chains, they are still effective biocides. I would read their recommended approach which is to shock first, then wait a few days and add PolyQuat. Though the remaining shock level of chlorine might break down some of the PolyQuat, that should still be OK.

What I think would be wasteful and be avoided would be adding PolyQuat and then shocking since the high chlorine level will mostly just break down the PolyQuat thus defeating the purpose of having an elevated chlorine level.