Yes, it should be possible. I say should because I didn't actually try that, but based on my previous experience with USB mice, the +5V for each optic board needs to be taken from different places on the mouse if it isn't taken directly from the incoming power source on the USB cable.
I used one of my mouse boards in my example, and since the USB mice boards I sell take the +5V from the original phototransistor locations, if taken from those locations they don't give enough "juice" to power simultaneous optic boards. I take the power from those locations because it makes the wire harness simpler with fewer connections. So, rather than re-hack a mouse to power all three boards, I opted to source the power directly from the PC power supply.
I realize that for your specialized controllers the method I used isn't very desirable, but my example is geared more towards a typical MAME cab setup.
When I get a few spare minutes, I'll rewire the harness to see if it will work all from the mouse.