I'm wondering if it's true that you can mine with a router. If so how well do they preform?
If you were hoping to do CPU mining from a router, you are about 30 months too late.
Now using one to control an ASIC, yes. Here's a related thread:
Avalon ASIC batch 2, OpenWRT, VirtualBox, IPv6-Hurricane Electric Tunnel -
http://bitcointalk.org/index.php?topic=146646.0