Most if not all poly mini-nucs I am aware of have some sort of mesh floor - if only to allow the bees to be introduced and for spraying water in to cool them when they are first confined.
Poly nucs for full sized frames do not all have mesh floors. One of the first, the so-called Canadian nuc, was a bit like a poly shoe box. However, I felt they could over heat in the sun if the entrance was too small - a hole about 25mm in diameter is the minimum I think.
Dampness was not a problem with these, even though they did not have any ventilation apart from the entrance.
But, if you have made these yourself out of straight poly insulation sheet it is likely the bees will chew it to bits as it won't be dense enough.