You are correct, but an RC circuit is part of the amplifier circuit and you can do a lot to improve the signal to noise ratio (SNR) depending on frequencies/signals are trying to amplify versus the ones you want to filter out.
I see, so you want to band-limit the noise, and are willing to accept potentially raising the noise floor in the band-limited range, the idea being that if the original noise is sufficiently broad-band, this will still increase SNR?
Fair enough: I was reading the original comment as referring to (thermal) noise intrinsic to the amplifier design itself (as opposed to noise due to imperfections in DC supply or due to coupling with some external transmitter), but this makes more sense, and we should consider the whole system anyway.
