A whole cloth quilt sure does count as traditional. I've entered a few shows and I've never had the sleeve critiqued, so just follow the show's direction and do your best to make sure it's straight so the quilt hangs well.
As for the binding, everyone thinks it's a big deal in judging, but it's not the whole deal. The Vermont Quilt Festival uses a point system and they only give 5 points out of 100 possible for binding.
I hope you do enter, and I hope you find it as much fun as I do - there's something wonderful about seeing your quilt hanging with all the others.
Janet