On reflection, I only get things that actually need a reply a few times a week, and probably a majority are automatic ones that are effectively spam. I'm an undergraduate student with a poor work ethic, so most of what I do is much less productive than checking email, and that plus being more-or-less friendless means I have some preference for getting some emails per day regardless of what they are - I should fix this, upon doing so I'd probably only be getting 1-3 a day, still mostly not needing a reply.
But your system sounds like a waste of a monitor, I could resolve to just look at the icon in the corner of my screen for the browser extension and click through to gmail once every four hours, and there must be some kind of equivalent for outlook you could use - why dedicate a whole second screen to it?
It doesn't take the whole monitor, there are five or six other things on that screen also left open. There are several advantages to it being open, e.g. it's slightly faster to drop files etc onto it in order to create emails with attachments etc.
It would probably not make a big difference if I did something like you suggest, however.
How frequently do you think you *should* check email? You can also say how frequently you do in comments.
Personally I'm sold on thinking you should check it around once a day, not necessarily without fail. That increases focus on both email and non-email, and minimises getting sucked into distractions. But some people I know disagree. Some believe in getting notifications whenever a new email comes in.
For anyone who'd like to check email less often and uses GMail, I recommend using http://inboxpause.com/ and this full screen compose link: https://mail.google.com/mail/u/0/?ui=2&view=cm&fs=1&tf=1&shva=1
Edited to add: I'd recommend everyone at least try checking only once a day, at least for a few days, to see if you find it more productive and/or relaxing. That'd be a big enough win to make experimenting worthwhile.