Lawrence Solum tells us no.
Here is an early part of his insightful, multi-tiered post:
On the one hand, the RIAA simply cannot bring enough lawsuits to create a real deterrent effect. First, the number of suits is so small that the actual risk of becoming a defendant times the cost of settlement equals a miniscule amount. Second, the perception among users of P2P programs is that one can avoid any risk of suit by keeping the number of files shared on any one service below a threshold (usually thought to be 1000 files). On the other hand, there is no evidence that the RIAA is changing copynorms.
When the RIAA sends the message, “copying is theft,” they are fighting the norms. No one believes that copying is the moral equivalent of theft, because everyone thinks that private, noncommercial copying is just fine. Even the RIAA seems to have thought that when they agreed to the provisions of the Audio Home Recording Act that permit noncommercial analog copying. And the fact that copynorms diverge from norms about theft is rooted in the underlying economic reality–consumption of intellectual property is nonrivalrous, whereas consumption of tangible property is rivalrous.
So here is an alternative message that the RIAA could try:
Share with your friends, not with strangers!
In other words, the RIAA could try to get the public to see that P2P programs are the moral equivalent of giving away hundreds of videotapes or compilation tapes. Those activities are not socially acceptable. They may not be socially unacceptable either. Mass giveaways are rarely a social problem, because the cost is high enough to deter the behavior without either legal or social sanction. That is what the P2P technology changed. P2P enables the low cost mass gift.
It is worth reading Solum’s whole post, I might add he is one of the smartest bloggers out there.