If the ring tone has been modified to be louder than normal, I would say yes.
Most devices like this are designed so you cannot overdrive the speaker. The amplifier in the phone was designed to work with the speaker in the phone. It's when you go and modify things you can cause damage.
More likely something can get caught between the speaker and the case impeding its ability to move. If it is there long enough, you can damage the cone or surround.