Like everyone else is saying I also would have put on drugs. All my elementary report cards said, "Johnny talks to much in class!" With enough positive and negative reinforcement -- I learned to control my behavior.
I was an Honor Graduate of the Air Force Academy and a jet instructor pilot -- and a programmer in my later years! I hate to think what would have happened if I'd been drugged.
Seriously - nothing wrong with being a receptionist or a lot of other jobs. But college catalogs seem to be more like vocational training schools -- just a lot more expensive!
Technically, yes it is possible. However, it would require a massive amount of delta-v to rendezvous with a significant number of enemy sats. And, that doesn't provide any reason to make something that can return to earth. You could launch a vehicle capable of your proposed mission on a normal rocket. Also, the enemy would notice that you launched something that is visiting all of their sats. At least, they would know you were doing close-pass espionage runs. They will be monitoring the space near their sats to see if anything is on an intersecting orbit that they need to maneuver away from in order to avoid a collision.
You don't have to visit all of them in one mission and given the complexity -- why not reuse the vehicle (it would be cheaper). Regarding ground radar, it is not as easy as you think to keep a continual monitor and we probably have the best system there is. The X-37B also has a stealthy shape. The dual rudders is pure F-22. They said it was to fit into the nose of the Atlas for launch -- but it may also reduce radar signature.
This is just conjecture. On a 'big' war day we are going to want to disable enemy satellites. We have ground based interceptors -- but there can be delays in launch windows, plus the 'bad' guys are going to be on guard and can take some evasive actions.
How about our little X-37 with a cargo bay and manipulator arm goes and pays those 'nasty' satellites a visit right now and attaches a few pounds of high explosive with a radio detonator. When the war starts you push a button and they all disappear!
Just in case they send a maintenance flight up, our little bomblets can also be equipped with a radio controlled 'spring' that detaches them from the satellite. No one is the wiser.
Possible?
When you don't know what you are doing, do it neatly.
