I've sealed the inside of mine with a glue mixture (I know, 90% of the people say that it is OK, 10% say not to get ANY water near the MDF, and yet people have been doing it that way for a LONG time).
I *might* prime it while I still have the last side still off since it will be easy to do it now, but I won't bother painting it.
I got a bit of water on my mdf ,it sprinkled a bit while i was working , made little bubles, stuff swells up something awfull. I will probly just spray clear before i close it up.