For posterity's sake, I went back and did a little research. Indeed, gamepads are supported natively from Android 3.1 (Honeycomb) and beyond... at the OS level. However, that's not the only factor.
The device you're using must also have a USB port that is "USB Host" enabled. I found this out the hard way when I tried to hook my ZD encoder up to my gf's LG Motion phone (which, by the way, is running Ice Cream Sandwich). That device's hardware does not support USB Host on it's lone USB port, therefore, regardless of what the OS is capable of, I wasn't able to get the ZD (or any other USB HID device) to work.
This seems to be a rare occurance (most modern devices with modern Android OSes support USB Host) but it can happen. I have yet to see a tablet device that doesn't support USB Host, but again, it is possible, so check before you buy!
The good news here is that almost all devices support Bluetooth now, so one could conceivably fall back on that as a control option. Bluetooth controllers/keyboards are pretty common - though I have yet to see one that I personally would want to use...