When WiFi is connected, does Android use any mobile data?

Could it ever happen that somehow an apps insists on using mobile data despite having a WiFi connection?

Yes, an app can do this. There is an API that allows an app to bind itself to a particular network, and it could deliberately select a cellular network. This might make sense for, for instance, an app for managing your cell carrier account (though a lot of those are explicitly exempted from counting toward data plans).

Most apps, however, will not do this: it would generally be quite user-hostile to use up a user's data plan when they're connected to an unmetered Wi-Fi network.