I wouldn't say "should". I would say "may", or "might", or "may or may not". I'd give it 50:50.

If the first flight is on time (or no more than 15 minutes late) and if there are no other delays (e.g. with baggage delivery) then there is a good chance that it will work. If there are delays it won't work.

Another thought... does anyone know how check-in/bag drop is handled at OSL? Is it "per flight" or "per airline"/"per handling agent"?

If it's "per flight" (i.e. there is a dedicated check-in for every flight) then the OP is unlikely to have a long queue in front of him because most other people will have checked in - so that should work fairly smoothly.

If it's per airline or per handling agent (i.e., one desk shared by several flights) then he could find himself at the end of a long queue, and may have to rely on the kindness of other people in that queue to let him cut in front.