It should work, although I have found it's best to leave one PC connected to the router via a cable just in case there are problems with Wireless (you may need to access the router's configuration web pages and won't be able to do this if you don't have a wired connection and the wireless is up the creek).
Still, you don't have to do that. If the wireless network does die, you can take the laptop into room 1 and plug that into the router.
BTW, you may be better off securing your network. I initially left my wireless network insecure and somebody managed to get in using a laptop and a wireless network card. I suspect they had parked in the car park at the end of my garden (it's not unusual for people to go there, park up and just sit in their cars for a few minutes, so no one would have questioned seeing a car parked up with people in it.
For info on securing your network, go to
http://www.cableforum.co.uk/board/article.php?a=12