Can you use a usb trackball on a hacked 360 ?

There are some options to use USB keyboard and mouse (of which this large appears as the latter) via plugins on JTAG/RGH hacked (as opposed to DVD hacked) 360s, and even without that there are keyboard and mouse adapters you can use to do things here though I am not sure how useful they will be for most things you are likely building an arcade cabinet for (most of the time they relied on custom tweaked inputs to work with FPS games, do most of the old school arcade expecting pixel perfect and... eh).
I am not sure what became of the JTAG/RGH plugins -- development started as an aside on one of the more hardcore hacking sites (as in the people that made the JTAG/SMC/RGH stuff hung around there) and sort of stalled compared to the USB adapter scene before RGH popped. Was still a thing you could do though.

Homebrew should support whatever it supports, though not sure what there is to merit looking at here.