Yes, but don't do it like you are suggesting.
Log onto the admin pages of the second router, disable DHCP so it won't assign anything that connects to it an IP address and change the routers IP address so it's on a different subnet than the first router (by that I mean, if the first routers IP address is 192.168,1,1 change the second router to be 192.168.2.1)
Then connect them together using the normal network ports on both routers, do not use the cable port.
What will happen then is anything that connects to the second routers wireless will get it's IP address assigned by the first router and the first router will be used as the gateway.