Wi-fi calling questions

I have poor cellular service in my home. No big deal, the wi-fi calling works great for me.

My question is, if I turn on airplane mode to kill the cellular network and just rely solely on wi-fi calling for communications, will my iPhone 5s always keep the wi-fi chip on to monitor incoming communications? This includes push notifications and phone calls. My main concern is while I am sleeping and my phone sits in standby next to my bed (usually not charging).

As an example, I woke up in the middle of the night to find that wifi was still on and connected, but it no longer said T-Mobile Wi-Fi at the top. Reminder, I had airplane mode enabled with only wifi active. Any reason why it would have disconnected from the wi-fi calling overnight?

I hope these questions makes sense. Thanks!