Will beeping dc motors cause damage to the motors?
Summary:  Safe enough unless you try really really hard to design it to be destructive. 

It MAY be possible to damage the motor this way if you tried hard enough, but that applies to any use of the motor, and it will be very easy to implement such a system without harming the motor.   Controllers usually have inbuilt hardware or software mediated protection systems which prevent one applying excessive levels of stupidity. Even without this it would be hard to destroy a system at sensible power levels. 

Issues may include 


Causing excessive thermal dissipation by applying high energy levels without the cooling usually afforded by the propellor downdraft
Operating the motor at zero revs is its potential highest torque point - if you were going to break something this will be a likely region to do it. But, any system not designed to easily withstand peak torque, even repeatedly applied, is not a well designed one.
Operating a motor in reverse applies reverse torque to the propellor to shaft coupling. Some systems use appropriate sense left or right hand threads to lock the propellors in position. Even almost zero revs reverse torque will tend to unlock the propellor - BUT it will be locked again by the next half cycle of 'sound' drive. and properly locked again when normal motion is applied.




Bonus:

For "extra points" you may be able to make it talk.
"Help me. Help me. I'm over here ...".
(I've heard of road surfaces designed to make a car's suspension "talk" - decipherable "speech".)