Can a rough-in valve for a tub break?
If you mean leaking from the tub spout I don't think that's likely. In those ceramic disc cartridge valves all the turning on and off is contained in the valve. There's no mechanical force applied to the rough-in portion to wear it out.

Are you sure all the o-rings on the cartridge are in place and intact?

I think your best bet would be to call American Standard to help diagnose the issue.