If you're asking whether it's possible to perform Umra with a visit visa: Yes it is and most likely you won't be stopped at the check points before Makkah & Madinah.
If you're asking whether Saudi law allows you to do that: No it doesn't. And I feel you wouldn't really want to break the law while going on a spiritual journey. In the unlikely case that you will get stopped you might face problems on top of that.
If you do get stopped, just tell the security guards you'll pray for them if they let you go.... :P