Is it possible to fly with throttles staggered?
Yes it is possible - as mentioned in a comment, most multi-engine aircraft can (fairly) happily fly with one engine at idle or disabled entirely.

Some autopilots will use some asymmetric thrust for yaw trim, and others will use asymmetric throttle settings to compensate for the engines producing different amounts of thrust. Those sound similar, but aren't quite the same thing.

For example here's a description of that happening on the 777. Neither are ubiquitous and both depend on the aircraft.

http://www.flight.org/the-boeing-777-thrust-asymmetry-compensation-tac

Note that two engines can never be identical, there will always be some level of asymmetric thrust. Traditionally this was countered with rudder trim, but newer aircraft sometimes adjust the throttle instead, as per the above link