I use mine with batteries. There's noise under the notes as it decays, hardly noticeable but once you hear it it's annoying. It's almost like a 'breathing' sound and at first I thought could be noise created by the limiter but it does it when just using one of the pre-amp models. It kicks in about half a second after hitting a string and decays and comes back as the note fades until it breaks up and the note stops, at which point it sounds a bit like an aggressive noise gate would.
My 'clean' patch is the Avalon DI model with the tone setting off, a reverb and limiter, but you get the noise with everything turned off. So I don't think it's to do with the effects themselves but the digital processing of the unit as a whole. I doubt it'll be noticeable though an amplifier to be honest, and for the price it's a great little tool but not 'studio' quality; hardly surprising for the price though.