Yup. Shoot down or disable the com sats (using technology we sold them), or real strong EMP near the Command trailers and the UAV is flying blind.
I believe the aircraft are programmed to return to base if they lose communications, but the mission is over.
A few more years though and we'll probably see "launch-and-forget" or "smart" UAV's, that will not require ground or sat comms to do the mission, and which have hardened electronics.
I have my doubts about that. You want human judgment in the mix when you pull the trigger; the situation on the ground might have changed since the UAV took off. It might get to the point, though, where the UAV does all the flying and targeting,and all it needs is someone on the ground to press the "go" button.
Unless the controllers are sitting in an AWACS sitting 400 miles away from the action, but with line-of-sight communications to the UAV