You can hear it plugged in with enough gain.
It drove me crazy on my 7-string for the longest time, especially with that low B sitting down there. Artist is right, though, it's the trem springs vibrating sympathetically to the string vibration. It's a pretty easy fix- simply mute the strigns with something. I tried stuffing them with cotton wool, but that wasn't a terribly elegant solution, and i think it messed with bar return a certian amount. currently, i have a folded up peice of paper towel tucked behind them, and this seems to work reasonably well. Not much pressure, but just enough cotnact to deaden the worst of their vibrations.