OK, I gave USB OD a try in Lion and ML. Here's what I found works properly:
1) The mouse setting doesn't affect EE unless you're trying to map keys that are also bound to the mouse into your gamepad. Usually this isn't a problem since most game devices show up as Button1, Button2, etc and not keyboard mappings (notable exceptions: Nostromo Gamepad, N52, N52TE, Logitech external "gamepads" that use keyboard keys).
2) The gaming device must have an Application Profile set to "All Applications", and the "Enabled" checkbox deselected. You will need to create custom profiles for any other games outside of the RB apps/emulators that can see HID devices. Customize those to your heart's content, since they will not be enabled unless those specific apps are launched, and because you disabled the "All Applications" profile completely, outside of those customized apps USB OD will not attempt to control the gaming device.
3) If your control device has an analog switch/button to change modes, you'll want to turn this on, center it in another app as I noted above, and then enter the RB emu of choice and configure the device. You should be able to click Set in the Joystick tab for whatever emulator button function you want to map and press the corresponding button on the game controller/device. Failure to rotate the analog stick(s) as noted above can result in menus not working right because one direction is always being "pressed" until the stick is centered. Failure to turn on the Analog mode if your gaming device has one will result in the DPad functioning incorrectly as a hat switch more often than not.
4) Check to make sure your device address matches in the two sections like in the pictures below. Take note of my "Aleph One" setting how it has an address of 0xfd510000, but the other gamepad status window shows an address of 0xfd310000. The "status" window is correct, but my "Aleph One" profile is not. That is because I moved the device to another USB port since then. This is critical since if the status window's address does not match the profile's listed address, USB OD will not handle the device properly (or at all) and EE can't use it because USB OD is trying to manipulate it. Delete any profiles that have addresses that do not match the Status window's address.
This should enable EE to coexist with USB OD, and is much preferred to using any other controller software if you need USB OD for mice as well.