Depends how close to c they could get. Minus bending or tearing spacetime, all it would take is energy.Either they can bend space and the lifespan doesn't matter, or they can't.
1000s of years? Try millions or billions. It would have to be, if they can't travel faster than light.
We already would be able to get a drone to our nearest neighbor, if navigation is your issue. How difficult would it be to navigate to the nearest 100 stars if we could literally wait thousands of years in a single lifetime to get a response?And still, you have the problem of observing the destination before launch. If these are random drones, the odds of encountering them pretty much remain at zero.