I've only every had misery where MDF and moisture can come together ... for that reason I'd never risk what you may be about to do.
It swells, it warps and it deteriorates ...
Whatever you plan to seal it with ... test sealing a piece of MDF with it and stick it in a bucket of water for a week before you consider it "good enough".
The only real problems occur is when veneered mdf is routed or not edged/lipped thus leaving just the finish (varnish/oil or two pack) protecting the mdf core.
Anytime the finish gets knicked or chipped can allow ingress of moisture. Solid wood sucks moisture in more readily through end grain, not so fast with face and side,
due to the wood cells design; mdf consists of pulped wood fibres and those little suckers (pun intended) act like a sponge, especially noticeable at board edges.
If the edges of the doors are to be routed with a decorative detail then the lipping material ought to be a few (3mm+) greater than the detail.
One of the worst things, both in looks and practice, is to route a faux panel into veneered board.