How does iOS handle a connected Wi-Fi network that loses internet access?

I'm trying to get my head around how iOS deals with a known Wi-Fi network that suddenly loses connectivity to the internet. If I'm connected to a network that's functioning normally and the network suddenly loses access to the internet (but the network SSID is still being broadcast), iOS appears to fall back to a cellular connection (if available); the Wi-Fi bars completely disappear from the status bar. When the Wi-Fi network regains internet access, however, the Wi-Fi icon then re-appears in the iOS status bar.

In this case, does iOS in fact stay connected to the Wi-Fi network in question but recognises the fact that no internet connectivity exists so falls back to the cellular network and periodically checks for internet access from the Wi-Fi network, or does this work in a different way entirely?

Yes, in this case iOS does stay connected to the WiFi network and periodically checks for internet connectivity.