Would a duffel bag like this be appropriate for swimming?

I use a Nike bag and it is fine. But neither mine nor this one appear to be "waterproof." In addition, this bag doesn't appear to have any mesh areas to allow damp things to air dry. In my opinion the only thing that really makes a difference is the bottom of the bag - is it water resistant? Some bags have an inner board that's wrapped in nylon - sometimes it's plastic, sometimes it's cardboard; plastic is ok, because the water isn't going to ruin it. Get some zip lock bags for things like your cellphone, ipod, etc.