It is, in fact, possible to mine over wifi. I picked one of these little guys up yesterday and all it takes is just a little configuration to get it to do what you want.
Under the hood this thing runs OpenWRT, and there are lots of walkthroughs online for connecting to wifi networks as a client. The basic gist is to
use the GUI to scan for existing wifi networks, and click "Join". This will create a new WWAN network. You want this to be in the WAN firewall zone. (These routers have two zones, LAN and WAN, which govern how traffic flows and gets NATted.) Then you want to disable the existing WAN interface, which defaults to the physical port eth1. Last, modify the LAN interface to bind to eth0 and set up DHCP.
Back up your configuration before starting
Also note that once you commit these changes, if you did it incorrectly you may wind up cutting yourself off from all access.
If you run into any issues I can try to help.