The exposed wood won't really be a problem, undercoat/primer is mostly there to make paint stick, which generally isn't difficult with wood, but more important with metals and plastics like on automobiles.
Any areas where it's showing through will look furry after the first top coat application. Successive coats and sanding in between will smooth it out.
I would keep going to get rid of the orange peel, if you can see it now, it will definitely show up in the top coats. I'd probably be tempted to do another pass with undercoat after getting it flat and then giving that a flatten as well.
The more work you do getting it spot on now, the better the finished result will be, with painting, prep is 90% of a good final finish.
Make sure you give each coat a decent amount of time to dry or you will find the finish will sink back into the grain a few months down the track.