The mail app does not support push notifications for gmail and also does not support IMAP IDLE (my naive understanding is that IDLE keeps a socket open and potentially the radio as a result which would impact battery life), so it fetches emails on a timer. AFAIK the only ways to get push notifications is with iCloud email and with an exchange server. I know you used to be able to set gmail up as an exchange server account on iOS, but I’m not certain if gmail will still pretend to be an exchange server these days. This is probably my biggest complaint with the mail app — like I said, it’s not great :), but it’s good enough for my purposes right now.