Level is the attitude of the aircraft relative to the ground and this is what you are setting up when you level the aircraft to initialize the gyro. With an aircraft airspeed and airfoil shape will effect how the airplane fly’s even with a gyro. The gyro sets the attitude and at a given airspeed the aircraft will fly straight and level but lower the airspeed and the aircraft will descend straight and level. Certain airfoils like a lifting one will have a greater tendency to climb at increased airspeeds even if they are at the same attitude.
I have used this property to stabilize the climb rate of my glider tug. It’s a tail dragger so I place a setup block under the tail wheel when initializing the gyro. The gyro is mounted on a board that is hinged at one end and raised or lowered at the other with a servo. The servo is actuated by a rotary switch. When the glider and tug are in the air the board is lowered until the attitude of the tug reaches maximum angle of climb for the glider being towed. Turns are mostly rudder only and gentle. At the top of the tow the board and gyro are again leveled and the tug tops out with the glider releasing. The gyro and board are slightly raised and the throttle reduced and the tug adopts a nice nose down attitude as it glides back to the base. The gyro makes the whole thing very uneventful. The tug has a modified Clark Y airfoil so there is a lot of lift and before the gyro it was common to almost stall the tug under tow at altitude where it was harder to see the attitude of the tug.
I use a block of a known length under the tail wheel to set the attitude I want for the aircraft. The length was determined by trial and error to get what worked for me. Being able to adjust the gyro in flight compensates for any airspeed or pilot.
Dennis