Do Android tablets generally support USB to Ethernet adapters? And if so, which models?
To my knowledge, the Motorola Xoom does support the USB to Ethernet adapter solution, but I don't know of any others. Even the Xoom however requires some serious work, and you will need one of two custom kernels for the Xoom as well as an adapter based on a particular chipset. For more information, check out this XDA article and the threads it links to.
I'm using a Toshiba Thrive (OS 4.0.3), a Curtis KLU MID704 (OS 4.1.1, and one of the Rockchip clones) a Polaroid branded PMID704 and a ZTE phone. Of all these, the Polaroid and Curtis have Ethernet support in the settings. I'm using a Radio Shack Belkin USB-to-Ethernet adapter, which is supported off-the-shelf by Android. (Only the Toshiba Thrive has a full size type-A USB jack.) The Polaroid is "broken" in that the Ethernet doesn't work. You click on it in settings and it clicks but does nothing. The Curtis works, it shows me my IP and MAC address in settings and I can set static IP parameters including IP Address, Gateway, NetMask, and 2 DNS servers.
However, the Android frameworks (in the Java(tm)-like language) are broken. The connection managers only support WiFi and Mobile Data. You can inquire about the Eth0 device but can't open a connection or do anything with it.
I know...I've got a $70,000USD contract hinging on solving the ethernet connection problem and it's getting frustrating. I've got google people telling me it's in there, but I can't find API's or examples. Supposedly Google's working on it.
Looks like 'no', with some xda-developers work. If you want to connect to a LAN, why not go with an access point the size of a deck of cards? If you want extra security, you might turn off your wifi router's beacon, use WPA2 without WPS, and turn on its MAC address filtering. Your device will connect without the beacon if you 'Add Network'.