Ok, so what you have is a pipe chase from the basement to the second floor and you want to fish some NM up through it.
I've done it but I don't like it. Don't like the idea of pvc jacketed cable in contact with a hot water pipe. UF wouldn't be any different would it.
If you can't insure that they will not contact the hot water pipe I would be more comfortable with AC or MC and it's metallic armor. I really don't think it's worth cutting up the plaster for this though.
-Hal
