If I understand things right (big IF) stethoscopes do not amplify sound, only conduct. So it would be the same as holding the egg up to your ear.
Correction, they do amplify a little via the diapragm in the drum of the stethoscope. The surface of the the working end makes poor contact with the egg and all you can hear is a scratching sound of the shell on the scope surface. If you made a soft adapter to fit over the end of the scope to cushio the egg, it might work. I only know this becuase I have a stethoscope, and i just went to the incy and tried it on a 17 day developing egg.