Casual copying between friends will probably increase, but I can't see it being any more common than lending or selling print books. Commercial piracy (e.g. torrent sites) won't be swayed one way or the other.

The move would probably help publishers to retain existing customers, because there is a lot of criticism over the limitations of DRM and that DRM is probably pushing customers to look for books elsewhere (both from legal and illegal sources). Judging from the comments around here, many of the people who buy DRMed books end up removing the DRM. That reflects a dissatisfaction or lack of trust with DRM, which doubtlessly makes those customers much easier to lose.

I doubt that the move will help publishers snag new customers. The biggest criticism I hear from people who haven't made the jump to ebooks is the price of ebooks. Every last reader I have talked to believes that ebooks should be cheaper than print books. Most of those people believe that ebooks should be significantly cheaper. Removing DRM ain't going to fix that problem.