Why not just set up phone notifications and deal with emails as they come in when you happen to use your phone? You never miss anything that way. Works great in my experience.
I have a friend who believes this way. If he doesn't stop telegraphing that literally every other distraction in the world is more important than me, we're not going to be friends much longer.
My boss at one company would call meetings with an agenda that he set and then step out of the meeting to answer phone calls from his boss. Then six or eight of us sat around trying to figure out what to talk about without him not there. Tremendous waste of time. Several man hours per incident. And if not for that personality flaw I would have called him a good boss.
That sounds like a bad way to live - I don't want anyone (and especially marketing nonsense, which is so much of the email that I get, despite me flagging all of it as spam) to be able to interrupt me at any time (still wish I could send all non-contact phone calls directly to voicemail).
Brilliant way to turn your brain into jelly/scrambled eggs! Never finding flow, never having a deeper thought, always be interrupted... I can't understand how someone could want to function like that :O