Android Tablets: Use USB to Ethernet connector? Do Android tablets generally support USB to Ethernet adapters? And if so, which models?
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'.