Login to AppStore over cellular data, jump on public wifi, download/install app is "safe"?
Your scenario won't work I'm afraid, because a TCP connection is created between a source IP address and port, and a destination address and port.

In your scenario, your phone's source IP address would change when switching network interfaces. This would break the connection, so the App store will not recognize that you already connected before, even though you securely connected over TLS (HTTPS)