The ENnies don't influence my purchases. However, I'm already pretty aggressive about chasing down publishers for review copies of the buzziest titles well in advance of the ENnies.
If I completely gave up on reviewing I'd probably take a look at the nominees and see if anything grabbed my fancy. I could easily imagine discovering the occasional gem through that, especially with so many judges working to talk about why any particular game was nominated.
As far as the publisher comments, I was always of the impression that it's hard to know what marketing really works. While the ENnies aren't about marketing, that's likely the major draw for the participating publishers. I write almost exclusively comped reviews. I very regularly know that friends, online and off, purchase (or don't) books that I review. I can't prove that, though, and it's not like a sale from IPR includes "Hey, C.W.'s review influenced this purchase" along with the money for the publisher. Ultimately, I think it comes down to where a publisher thinks his or her money is best spent in this small hobby of ours.
It's worth noting that the IPR guys seem to think so highly of the ENnie awards that they put out the Summer of Revolution promotion every year now where they try to rock the vote for awesome indie endeavors. I think the amount of time and effort there says a lot about at least some small press perspectives on the awards.