would they get a stress if in arc?

Choppers ability activates at the start of the combat phase - Zeb's ability happens during the combat phase

So chopper can bump (or allow himself to be bumped) during the activation phase - At the start of the combat phase he stresses the bumped ship(s) - then when it's Chopper's turn to shoot, Zeb allows Chopper to shoot the ship that he is in base-to-base contact with - provided it is within arc.

Note also that Zeb also allows enemy ships in base-to-base contact to shoot back

would they get a stress if in arc?

No, if Chopper's ability counts as activating during the Combat phase.

Usually, activating during the combat phase is the "Its my turn to attack" bit.

Choppers ability triggers at the start of the combat phase, zebs ability doesn't trigger until one of the ships activate during the combat phase, so the stress gets dealt.

"Start of the combat phase" is a specific period that occurs before any ship activates, so Chopper's ability wouldn't be affected by Zeb's.