I've been running my TCX on my TCXX option chassis. If you add 2mm to your ackerman spacers you get the same arc as when it's on the TCX.
As goots says, it won't mimic the TCXX arc without the longer arms.
You won't be able to screw the rack brace to the top deck, but I've never seen anybody do that anyway.
All that said, I think my TCX feels better on the narrow TCX chassis than on the TCXX option chassis.