I know it's possible to get interceptors to move around without having carriers present (for an extended amount of time that is) but is it possible to get those same interceptors to attack in that state?

So far I've only seen them move around.

They can only attack if a carrier is near. Without a carrier they will explode.
Btw, if you freeze them, they will shot more often. that wasn't your question, but I try to spread my knowledge.

Really? I should try that sometime, you could have the carrier hidden out of view, and have them stuck, like some kind of defense.

Just a question.

If a carrier is attacking with interceptors and gets stasis fielded while doing so, what happens to the interceptors?

Freeze, as in Move Unit to location, preserver, or disable?

Move to location, and if you freeze the carrier with stasis the interceptors will automatically return to it.