If I use the addspell function ([ActorID.]AddSpell EffectID) in a quest script, does it interupt the quest script, then come back, or does it get queued and processed later?

The quest script will continue to run to its end. Can't say with any certainty when the spell script will run other than after the quest script completes its execution in that frame. I would guess that the spell script would run in the next frame, and not the current frame directly after the quest script ends. You could test it using PTC if you really need to know.

Thanks. That answered my question.