What will happen if I try to apply paint/stain to damp wood

I'm 1000 miles away from home working on a deck for a family member who recently suffered a stroke. He's recovering, but for the time being he's very unsteady on his feet. The deck in question had a lot of mold, and was very slick when wet. I've already pressure washed and cleaned the surface, so that the mold is gone and it's no longer slick. That was the main goal — in his present state, the deck was outright dangerous; now it's much safer.

However, the deck wood now has no protection against rain and moisture… I just stripped it all away 🙂 If I don't also do something to protect the wood, it'll be slick again in no time at all, not to mention start to rot. My problem is that I'm only here for another couple of days, and the weather is not cooperating with finishing the project. It's dry enough to get out and work without getting rained on, but not enough for wood to dry out. After the last scattered rain, there is no chance it will dry in time for me to do anything before I need to begin the journey home.

I have some Behr Deck Over, which I reckon is either something in between a paint and a stain or just a thick paint. The hope is that it will hold up better and protect against moisture like a stain, but cover the surface more like a paint — and not show the few remaining bits of old paint, as I was time-constrained in the removal, as well. But still, the wood is kind of damp. At this point, given my time constraints, I'm considering applying it over the damp wood.

My questions are, what will happen if I try to apply this to damp wood? What are my alternatives? Is there anything I can do to improve the chances of a good application? I'm really looking to see if someone will talk me out of this before I do something dumb.