it depends on how you're setting up the computer and wifi router. if you're wanting to run a router/firewall OS on the computer then yes that setup should work as long as you can disable the DHCP role on the wifi router (ie just have it set up as an access point). if you're running a standard desktop OS like Windows 7 then I'm not sure how that would work. maybe adapter bridging would work, it's not something I've come across before!
if cable distance is the reason why the wifi router is not going into the modem then maybe having a small 5 port switch by the computer is a better solution. it means that the connection will be always up even when the computer is powered off and the connection will be more stable.