After reading over Agents and Drones ( 246 and 265-270 SR5 Core) which i suggest you do. I would say you cannot have an Agent run a drone, pilot programs are what do that. Agents are designed to operate on the matrix only, you could I expect have an agent attempted to hack a drone. But that's not here nor there.
Does it change things with a pilot programming running the drone vs you? Yes. As odds are good that comparative stats and skill ratings will be very different. Jumping in is generally more effective then just sending a pilot program, though it of course entails more risk, and depends totally on how you built your character.
Does it give you more freedom to let a pilot program run your drones? Yes. Though that's possibly false assumption, given freedom isn't well defined there. There would be different sets of actions available under each set of circumstances. But one would include what amounted to a NPC with what is described as dog-brain trying its level best to follow your orders.
If you order an agent to run a drone? See above.
Sprites are arguable a different animal Machine sprite might well be trainable to operate drones, given a cooperative GM. But that's really a whole other set of issues.