When you compress you're turning the whole signal down, noise included. The balance within
the audio doesn't change. But as you've added make up gain to bring the compressed signal
back up, the noise will be louder when the wanted signal is not present. Eg between words
in a vocal, as the compressor recovers you're left with uncompressed source with added
gain. With a fast release you're going to be bringing up a lot of detail on the quieter
words and in between words, and that includes noise.
But in the context of
most modern production styles, noise is really something to get too worried about unless
the recording is really noisy to start with.