I doubt it. It's not their position to try and sue you for other people's stuff.
You'd probably be ok with bootlegs (80/90s defenition of bootlegs) though.
If you download music that's not been through the RIAA then you could be ok, they don't have as much power behind them as the RIAA do and it only seems to be the RIAA that's really going after the downloaders.
