Class Action Complaint Against RIAA Now Online
As for "shutting them down", I seriously doubt it will be that drastic - a win here would definitely start pushing things in the right direction, but this is civil law, not sports.
As for "if they win, we are screwed", as above it wouldn't be that drastic either, it would push things in the other direction. However - and IANAL, just a criminal justice/IT student, I'm willing to bet that if it started looking like the RIAA was going to start winning, it could be withdrawn. (the RIAA cannot withdraw it if it looks like they're going to lose, because they didn't file - that doesn't stop the other, plaintiff party, from withdrawing)
Legal crap like this is never so clear cut - it's usually just a big goatfuck no matter what side your on - the only winners are the lawyers.