Will the full size mags fit/function in a 320 compact model?

Yes, they will, with a qualifier. I've never had it happen, but some have reported jamming a mag into the well, with the slide locked back, and damaging the ejector. The ejector is part of the FCU assembly; it's not replaceable as a component, so the damage is expensive.

if the mag is inserted with the slide forward, it's a non-issue. If the slide is inserted until it locks, without jamming it home like one is pile driving the support for a 70 story building, regardless of the slide forward or locked back, it's a non-issue.

It makes sense if carrying the compact, to carry a full size magazine as a spare (or two). I do.

Carry the 21 round magazine. That makes a great spare, too.