Dude, I am a fighter guy and as I type this I just got off shift at the CAOC (combined air operations center) in Qatar keeping watch over Iraq so here are my thoughts:
While I don't know the exact number of hours of use, UAVs are being used extensively. Not only by the Air Force, the Army has their own as well. These assets provide a capability that are of tremendous advantage to the ground commanders (Army and Marines) and also provide incredible amounts of information to the intel world as a whole for planning and conducting "other" things as well.
The arming of these assets is extremely limited and their long on station time generally prevents serious weapon loadout (things that will actually kill and destroy things). This doesn't mean they won't be able to figure that out in the future though. In fact, if they could carry some real bombs while retaining their current capabilities, they would be the ultimate COIN (counter insurgency) aircraft and possibly CAS (close air support) aircraft in a permissive environment.
Because of the UAV's inability to carry significant destructive loads, fighters are still the preferred aircraft when the boys in cammo are doing some serious work. F-22 and F-35 are the jets of the future along with the higher block F-16s and F/A-18 E/F that will stick around for a while and none of those are planned to be unmanned at this time.
As the future progresses (thinking 30-40 years here) there may indeed be less manned fighters and big bombers. Despite that, there will be a need for a long time to have manned aircraft for the dynamic large force environment. Satellite relays take time to process information, requests, and aircraft commands - the speed of light is only so fast when trying to operate jets from half way around the world and bouncing signals off of satellites.
UAVs will replace some assets, but not all. I think they are mostly an enhancement into areas that we didn't even think about 10 years ago. That might lead to fewer military pilots overall though and contribute to the pilot shortage you are referring to as I don't think anyone will be allowed to count Predator time.