Yes, Design 3D CX 7 will run on Mountain Lion (Mac OS 10.8.x) and Mavericks (OS 10.9.x).
However, if you have CX v7.0.4 or earlier, the serial number will not be retained when you quit and then relaunch the software. The solution is to update to version 7.0.7.
Apple changed some things in Mountain Lion (Mac OS 10.8.x) having to do with our ability to write the serial number to the hard drive. We have released an update to the software that fixes this issue, along with many other fixes and minor enhancements.
The CX 7.0.7 update can be found on our free updates page: http://www.strata.com/support/free_updates/