If you have to ask... then you probably suspect the answer.
If you can't do the time, then don't do the crime.
Don't touch this URL with your own computer www.riaa.com/issues/music/downup_faq.asp and for goodness sake, don't keep their cookie; they'll want you to pay for it.
Supposedly you can make copies of your music for your own use only. One use could be to place it somewhere for redundant backup, like at your friends' houses, and on DreamHost's server. Probably should have a written exchange-protection agreement, and only 2-3 friends seems more reasonable.
Are you asking does DreamHost scan their servers for presence of mp3s? Does r1aa track downloads? Will they take pre-emptive action to get you?
Sneaker net might be safer. Or just don't do it. You might pay in the next life too.
Hey, why'd the lights just go out?! What's that crashing downstairs?!
Honey, start the therm1te!