Haven‘t tested that yet. But my gut feeling says no.Interesting. I mentioned earlier that the devices connect to Google and seem to do something that registers server-side, but not locally. I thought it was just the calendar that did that, but I use iCloud for that so I couldn't really confirm.
Does setting iCloud to fetch as well solve the issue for you?
By the way, any chance that you have restored your affected iOS devices from previous backups? I haven‘t done a clean install at least since iOS 12 and I suspect that might be the issue. The stock Mail App has long been unstable and flaky for me (e.g. it often complains about server credentials) in combination w. Gmail. Maybe it‘s time for a clean install.
And yes, there might be something w. switching connections. At least when using my iPhone on WiFi only Mail stops refreshing. I have to confirm that happens on cellular too.