Shouldn't be a problem as long as you 'qualify' the appropriate python.exe with which to run your scripts.
Your bigger consideration is whether your scripts are compatible with your chosen version of Python....arcpy was developed to run with 2.7 at 10.1, I think, and while there are other versions and flavors, it is generally not recommended to install those as you may run into some unanticipated problems or 'side effects'...
Enjoy,
Wayne