Psx to usb dual mod xbox360

Is it possible to use a psx/ps2 converter to do a dual mod with a xbox 360 CG pcb.

for example:
PSX control > converter > (ps3)USB (which now makes it D+, D-, Ground and VCC)
and the common ground xbox that already has D+, D-, Ground and VCC

use a switch for D- and D+ while connecting the ground and 5v on both pcbs so I can run it through one cable.

I would like to avoid using a converter for this but I have found no answer as to if this is possible.

I suppose it could, but why the hell would you want to???

I just figure it would be the easiest method to run one cable. The converters I bought were only 4$ off of ebay so I don’t mind sacrificing one. I have 3 psx pcbs lying around and I don"t want to build 3 psx only arcade sticks or use a db25 as I planned earlier.