What does "well connected" mean? If they were really well-connected, you'd probably have funding... and VCs with an active interest in getting users for the product. Well-connected means that VCs who don't fund you will mentor you until you are fundable. It means that you can get TechCrunch coverage with a phone call. That's what "well connected" means.
Too many people sell themselves as being "well connected" when they aren't. 99.9 percent of us (and 99.99 percent of the smart ones) are peasant people who don't have that kind of access that would merit having a non-technical founder.
There is an alternate strategy to the "leave now" advice that you are getting. I'm going to explore it just for the sake of doing so, although the default advice of "quit now" stands. If these founders are well-connected, they can prove it. Ask to go to investor meetings and the various other high-society shindigs they attend to keep up their connections. They might as well, because it sounds like they're not paying you. If they do so, then you can evaluate for yourself whether they're well-connected enough to merit staying in this long-shot startup (and you can make connections yourself). Sitting in on the investor meetings will also give you a voice in technical decisions because you'll have your own perspective on the business needs.
Chances are, they'll say no. It's very unlikely that these "well connected" "idea guys" will let a lowly JAP (JAP = Just A Programmer) in his early 20s sit in on investor meetings. This refusal will make it clear to you how little this personal affinity/loyalty you feel toward them actually means... not much, on their end. If this happens, then you should leave without reservation or any feeling of guilt.