6550C, Classé amps with the exception of a couple multichannel and integrated models, all have output relays. Also, models from the CA series going forward have soft start circuitry that employs relays. They are responsible for the various clicks you hear.
The click after a short delay when you turn your amp on, is the soft start relay(s) contacts closing, to bypass a power resistor in series with the transformer primary. When you turn your amp off, the output relays open almost instantaneously, disconnecting the speakers, and preventing any turn-off thump.
Its apparent from the OP's description, that his amp does not have output relays. Turning an amp off while it is receiving input signal does no harm.
The click after a short delay when you turn your amp on, is the soft start relay(s) contacts closing, to bypass a power resistor in series with the transformer primary. When you turn your amp off, the output relays open almost instantaneously, disconnecting the speakers, and preventing any turn-off thump.
Its apparent from the OP's description, that his amp does not have output relays. Turning an amp off while it is receiving input signal does no harm.