If you use a RAW converter like Capture One, you can get away with pushing the exposure by a stop or a stop-and-a-half in either direction. Much more than that and noise starts getting bad. As you say, much better to get it right in camera where possible.
You're right, it is noise. This has probably been caused by trying to recover the shadow detail after under exposing.
There are a couple of reasonable noise reduction programs around, Google Noise Ninja for example.
Hope that helps.