Only if combined with a vigorous policing effort to stamp out piracy (which I fear may be impossible).
Most users (especially teens and early adults) are not going to pay $1 per track (to give a figure) downloaded from the official website if they can just fire up Kazaa or whatever P2P client and download the entire work of that artist for free.
The respect for ownership has gone down that much, it's no longer a cost issue but principle.
I've met people who were actually PROUD of not having any paid for music or software, but having it all pirated and leeched off the web.
Looking at what that software was a lot of it were programs costing $5-$25 each, not applications costing thousands which they might not be able to afford on their income/allowance.
Then there's the software engineers (individuals and companies) asking around for cracked versions of anti-piracy tools because they want to protect their own product (commercial...) from being pirated.
IMO that's the ultimate irony as well as the ultimate example of the mindset of many people these days.