You can do it however it is a gamble whether you create problems later. The automotive clearcoat is formulated to use on steel or fiberglass and if you happen to get a brand that is very hard it may crack from wood expansion. Wood finishes are formulated to be more elastic to allow for wood expansion. I don't use automotive clearcoats on wood so I couldn't recommend a brand that would work for you.
It depends on what type of clear you use and how it might effect the latex. Quite a few auto clears can be used on wood. Hopefully you have NIOSH training, since some isocyanurate catalyzed clears can kill you if you breathe any in. They react with water and will freeze your lungs, permanently. House of Kolor Kosmic clear is an option if you want high gloss.
There would be less wood movement with MDF but it won't be eliminated. It's one of those things you will have to try it and see. Unless someone here has first hand experience with a particular product they could recommend I still think it's a gamble.I'm using MDF, and I will prime the inside and the outside of the box.
I assume it will have basically no expansion?