Can't see any problem. We have NTL/Virgin Cable which is connected via a Scart switch box to my Akai DVD/Video recorder. The same machine is also connected to my Freeview box - hence the scart switch box, and both work fine. The Scart out goes to the TV from the switch box. The RF out is connected via a long lead to another TV in my Computer room and also works fine.
This is the box I use
I have seen it as low a s £9.99 from other stores but I have given this one as it was easuiest to find.