This works but should it?
 

I have a wireless router upstairs to which it is connected to the cable modem.
All 4 ethernet ports are used on the router, one of which is connected to an additional wireless routers WAN port. the additional wireless router, a Belkin N1 Vision shows it is connected to the internet on it's display.

This set up seems to work just fine, sort of a wireless repeater.
I might try a different SSID and passkey on each router and see if my wireless devices detect either.

Re: This works but should it?
 

All you're doing is double NAT'ing it will may cause problems with games and other applications that need specific ports and it will be slower..

Re: This works but should it?
 

It should work, and yes, it's likely to have lower performance and other drawbacks.