I'm not really sure if it keeps trying or not. If it does, I would assume it does the same thing as my phone does when I disconnect my watch on the watch side. It waits exponentially longer to poll for the watch each time to help conserve battery.
The easiest way to tell if it's connected back to wifi and dropped mobile data is to keep an eye on your icons at the top, by the clock. If you're connected to wifi, you'll see the wifi signal. If you're actively sending/receiving data over wifi, you'll see the little arrows "light up". If you're connected to mobile data, you'll see 3G or 4G (or whatever signal you're getting) and the bars. If you're actively sending/receiving data over mobile, those arrows will "light up" as well.
As android tries to be smart about helping you out and conserving battery, I'd be surprised if it just constantly polled to see if the wifi network had internet all of a sudden, but it's definitely possible.
It's hard to test such a thing though, without access to a "bad" network. When you have wifi turned on, but not connected, it polls periodically to see if networks are available, but I can't verify whether your device might label that network as a "bad" network and just try to avoid it. That's a newer feature of these devices and may or may not be the case in your situation.