No. If a system switched to a different AP, any existing connections would fail to work. That said, if you're not concerned about long-term connections (that is, it's only intended for simple web browsing) it would probably work okay, with only the occasional glitch.

A better solution would probably be to aggregate all of the internet connections with a separate router that can handle that, and then just use the wireless routers as simple APs set up to do normal SSID sharing.