First, what you're describing is in no way a "live with it" scenario. What you hear in playback is what you should hear in the mixdown.
That said, I'm not totally clear on what you mean by "noise." There are different sources of noise in studio.
The first is channel noise. If you record the track at a low level and need to boost it in the mix, you can introduce more noise (that's why a clean recording is always preferred). You can also introduce noise recording too much input signal and it's distorted at the input stage.
Second is process noise. EQs and plugins are not created equal. Clean plugins use sophisticated alogrithms to crunch the audio (with a hit to the CPU). Cheaper plugins can be lightning fast but introduce unwanted noise an artifacts.
Third, it could be something in mastering. If your master output level is low and you need to put the audio in playback, again, you're introducing noise to the audio process (in this case at the output stage).
Do you have a sample you can link to so I can hear it?