Will a GFCI outlet which is also on a GFCI protected circuit (GFCI breaker) work properly?

Maybe so but why would you have two on the same circuit anyway what a waste of money. It may or may not work depending on the amount of return on the outlet does not confuse it self with the return of the amperage coming back. This is how they work and they work on milli amps so they can be very delicate.

Merry Christmas

Yes , the circuit breaker will detect a fault just as the brewing system outlets will. This is redundant, but neither one should affect the other as far as detecting a fault and opening the circuit.

One may be more sensitive than the other and trip at a lower fault level. The standard 120 volt GFCI outlet is designed to trip at 4-6 Milli amps.

It should, if both are wired correctly. Try the "test" button.

I just tried a hair dryer, with a built-in GFCI plug, in a GFCI protected outlet. The "test" button on the dryer worked.

it should if wired correctly, a bit of overkill IMO.... i would much rather reset the GFCI receptacle than have to go to the load center (breaker box) to reset it.