Well I must say that I have never heard of someone using significantly snares. The only thing that I could imagine happening is that you'd end up choking up your drum killing all the response that makes a snare what it is. The snares run completely across the bottom of the drum for a reason.
Have you ever realised that when you play away from the snares on the he batter head (to the edges that the snares don't run) that the sound and snare response are very different? If you tweak your snare correctly you might be able to get a decent sound that is nice when you pop it in the center, but other than that, my guess is that the drum would be considerably less responsive.
I also consulted one of by buddies at my favorite drum spot, EXPLORERS PERCUSSION, and he agreed with me. The only thing he had to ad to this is that "your drum will sound like you're playing on a paper plate." He said this out of experience. He had his snares blow out on a gig and the only thing he had were 13 inch snares.
Hope this helps,[/b]