With the transmitter turned off, and the receiver not picking up any signal to try to make the servos "work", the servos will get no commands from your receiver to do anything and will remain quiet.

When you turn on your transmitter and receiver the transmitter tells the receiver to tell the servos to move where the sticks are indicating... usually center on everything except throttle (since that stick stays where you put it). Any tension against the servos when they are commanded into a position will cause the slight buzzing you hear. It is normal and should be nothing to worry about.

Now, with that said, the ideal situation is to have nothing causing the servos to "work" when the controls are centered. Have an experienced buddy check out the control setup in the plane to make sure no surfaces are binding and that no linkage is binding and the linkage is properly adjusted. Servos draw current when they work and if you have one or more that are constantly fighting to remain in position they will drain your battery faster than servos without a load against them.