Depends on the model. Generally, dried-out, heavier stuff will just settle at the bottom of the reservoir and come out pretty easy.
Anything likely to leave skid marks though might hit against the filter (again, depends on model) and leave residue there.
In any case, I think you’re asking for trouble b/c your rig is likely to stink to high heaven. And if you’re dealing with moist items, well, the cleanup is likely to require extensive work.
And remember, the air that’s sucked into a wet-dry vac is pumped back out. So if your container is full of 3-day old shit, that’s exactly what the air coming out is gonna smell like.
Instead, why not just grab an old plastic grocery sack, use it as a glove, grab the morsel, reverse the bag, and tie it off?