Yes - the usbhost_t36 driver does have Joystick support through the HID support. I have done some testing of it it with Sony playstation 3/4 controllers. I also earlier tested with a Teensy plugged in for a Teensy configured as a Joystick. I think these are in the released code.
Recently was able to get the XBox-One controller supported as well. But I believe this is still only in my code base waiting on Pull Request.
Note: All of these are currently only supported by USB cables. That is not through Wireless controllers (like Bluetooth for PS3/4). Not sure about Microsoft XBox PC Wireless adapter as I don't have one to try...