Tobzalp
You are correct that Global Hawk operates at high level where the only conflictions are U-2 and the odd other exotic/old aircraft. Additionally, it is very rare to see more than 2 operating simultaneously right now (although I suspect that this will change as the RQ-4 matures).
However, the Predator and others such as Hunter are down in the thick of it. Indeed, Predator particularly demands care as it's often to be found lurking below CAS stacks (ie just at the levels where CAS roll out of a weapons delivery profile and are preoccupied avoiding AAA and SAMS!
Regards,
M2