I wouldn't. I think that plastic wrap wouldn't be substantial enough to stand up to a month under wet substrate then still be strong enough to pull it out without breaking. Plus there are the concerns over chemicals and what would happen if the frog accidentally ate some of it.
I also don't think burlap or reptile carpet would be a good idea. Staying wet that long it isn't going to take long before you've got bacteria and mold growing all over it.