Upvote:4
I've never been asked anything by them, and I'm Swedish (i.e. also EU).
If using an ID card, you'll get a migration card with an entry stamp if and only if entering by land from Turkey (at least at the main crossing in Sarpi). If entering by air or sea, you will not get one.
However, the ID will be scanned and it will be put on record when you entered and (if entering by air) where you flew from.