I always imagine it creeping up on unsuspecting satellites like some kind of space puma. All up close and personal like, giving them a sniff and then slipping away undetected.
http://www.heavens-above.com/orbit.aspx?satid=40651&lat=0&ln...
If it was to get close to a non-US military satellite, one could expect people to complain diplomatically, at least.
[0] http://www.space.com/8470-secret-37b-space-plane-spotted-ama...
[1] https://www.universetoday.com/65338/amateur-astronomer-image...