Probably has some effect. Think I read somewhere that about 10% of households don't have checking and/or savings accounts, and a lot of those were said to be higher-risk demographics. Probably would keep you from getting instant approval, but I gotta imagine it wouldn't be a denial situation unless there were other flags to go along with it.

If nothing else, having a small savings account with Chase would probably help on the recon calls down the line, as you could enhance the "long-time customer" tactic.