The usual "procedure" is - the app notifies when it checks mail, there is no separate "notify me about new mail at ... hour" independent of when it's actually going to look for new mail.
The "checks mail" has two varieties:
- Scheduled checks - default to every 15 minutes.
- Push mail - off by default, but gets any changes (not just new mail, also messages being marked read, for example) near instantly, uses the battery somewhat more.
Normally scheduled mail checks should be quite reliable but but but....
For example, Android may decide to "optimize" the app out of being able to work in the background. Or there may not be a network connection at the time. Or Android may postpone the app's chosen time of the next mail check by an hour or more.
What I'd suggest, given all the above, is start with the default "check mail every 15 minutes" or maybe change to "30 minutes" or something. This really won't drain your battery.
The app also has a "nights / weekends" section in its settings, so you could turn off notification sounds at certain times of the day / weekends.
And then once you got used to that, maybe you'd want to tweak the setting to be "every hour" or "every 2 hours".
Does this sound like a plan?