This guy seems to have done it without issue. Makes sense considering duck hunters and all.
https://www.youtube.com/watch?v=8Dq7K5F3PZU
I humped guns in HI jungles plenty of times without any issue from moisture. If you're that worried about it, sling it under your poncho. This way it's still ready for self-defense use where you don't need to remove it from a sock/cover.
If it gets soaked, hit it the gun with WD40 (Water displacement), wipe it dry, and use CLP. Then wipe down the brass on the shells from the magazine and/or replace those shells with fresh ones. Let the wet ones dry out.
I don't think much of that is necessary but that's what I would do in the field if concerned. I would use a sandwich bag or condom on the barrel muzzle if you think you might get mud in there.