Yes and no. The tube can just fail and stop working with no other symptoms, or it can fail and cause a fuse to blow, or burn up a resistor, or destroy an output transformer. It depends on the amp. For what it's worth there are millions of tubes and tube amps in use and no major incidents.
Can using a bad tube hurt an amplifier?
If you're using a tube for a while, and everything's fine, and then voltage changes over time gradually, and then it damages an amplifier? are amps Built with controls to prevent that from happening?
How can you trust using a tube if it potentially could harm an amplifier?
Assuming You're using the correct tube in the slot provided.