Is an amplifier protected by the fuse or breaker if a lightning strike has possibly hit the amplifier's circuit?

The result of a nearby lightning strike are unpredictable.

If the strike affected the power line, resulting in a sudden spike of power, a fuse or breaker cannot possibly react quickly enough to save the amplifier. For that kind of protection you would need to install a surge suppression device on the power line.

But even if you have a surge suppressor, understand that EMP (Electromagnetic Pulse) caused by a nearby lightning strike can cause damage to CMOS transistors even when the device is unplugged. Typically that doesn't happen, but it is possible.

While the output transistors tend to be more robust, many of the low power circuits can be affected by lightning.

Beyond a surge suppressor on any inputs and power lines, and the manufacturers shielding, there isn't much you can do.