Would the local network administrator in my dorm be able to figure out that I'm using a WLAN router to access their wired internet connection? Assuming I'm not broadcasting the SSID.
Possibly. The local network admin can simply just walk around with a laptop and Wifi Packet sniffer like Kismet or NetStumbler and can pretty easily see any traffic is being generated within range. Not broadcasting your SSID won't protect you. Even if the traffic is encrypted, the MAC addresses aren't. MAC addresses are easily correlated to a manufacturer, like say Sony.
If you then record the MAC address, and look for it on the local LAN, you could then trace it down to an individual port, and an individual person. Even if you hide the MAC addresses behind a router, if your traffic goes across the wired LAN it'd still be possible to do traffic analysis, and correlate WiFi Traffic with traffic that then appears on the local LAN.
The short answer is, WiFi Traffic isn't a secret, and you can't easily hide it from anyone in range to pick it up.