It's quite possible, however, most cables have a limited length before quality loss happens, this length differs by cable and quality. Given RCA is anolog and wasn't designed with much shielding, I'd say 20 feet is the max length for it before quality degrades (hopefully that isn't an issue given the rooms are right next to each other like you said, just avoid putting it next to any power lines/sockets)
They are, and the tv in my room is actually against the same wall that my xbox is next to so it would be the same length cable. It would be pretty cool if Microsoft would make a splitter where you actually can plug two xbox component cables into it, it would just like the regular cable only the end would have a little box with two "Xbox" ports, this is where you would plug the end of each component cable, each one would go to a separate tv. If you don't understand what I mean the box would have two of these.
http://cdn1.gamepro.com/article_img/gamepro/128348-1-1.jpg
In which two of these would be plugged into.
http://img381.imageshack.us/img381/328/cableswitch5ia.jpg
The other side would just have one of the above things sticking out to plug into the one port on the back of the xbox. that way you could have one on hd and one on sd by simply changing the switch on each one.