So today I was messing around with a Raspberry Pi using Raspian. It turns out if you have an ethernet connection without Internet and a Wi-Fi connection with Internet, the Pi / Raspian is too dumb to figure out that it should use the Wi-Fi connection for things like dns lookups and web traffic. Slightly annoying. I'm sure there's a way to fix this - but time is not on my side today.
Update: It turns out it's more of a widespread linux problem. This morning on Ubuntu I tried connecting one Wi-Fi adapter to an AP that was not connected to the Internet and a second one that was. It seemed that again the traffic tried to take the path through the first adapter.