ok, we have 1.5" of MDF and you are wondering if a layer of poly about the thickness of paper is going to make the whole panel of MDF swell?? I don't THINK SO!

I think the OP was asking whether sealant on the cutout section would
swell the MDF enough to affect the fit of the insert. In response to
that, I doubt that the amount of moisture in sealant would cause enough
swelling to cause problems with your insert, but I know MDF does swell
when wet, so I'd use a couple very thin layers of something oil-based
that polymerizes to seal and protect from water.
Of course if you have any scrap you could measure it with a caliper or
micrometer and test a few different finishes - let us know how that
turns out.
Good luck,
Andy