I know you can attach up to 8 buttons to the u360's, so I wasn't planning on using an ipac or anything. Does the u360's allow for the shifted function?
Shifted buttons are
usually in the realm of keyboard based controls, but there's nothing to prevent them from being implemented on gamepad based ones.
But if you are just concerned with MAME, it doesn't matter. MAME has the ability to map functions to multiple button presses. Just pick an input you want to use as a dedicated "shift" and when you define those shifted functions, hold down your newly defined shift button and quickly press the button you want to assign to that function. Just be aware that it won't work outside of MAME, if you find the need to go that route.