yeah it will work, doubt it will increase the speed that your getting when downloading though. if it's very slow downloading it's likely your connection is slow, whats the speed like on your PC?
But if you want to use wireless then you can only use one wireless router.... not a wireless router running off a wired router... two routers is very bad (it's called double NAT) and is not really a favorable thing to have in networking.
Anyhow, make sure UPnP in turning on in the router admin pages and as long as you have only one router inline it should work.