Would be nice just to block the checking email notification or never have it show up in the first place. I honestly couldn't care less if an app is doing something in the background. Just really annoying having the spinning circle always there. Enough to make me look for another email app.
The only notifications I am interested in is when an email arrives or something is not sent. Everything else is just redundant.
This thread is several years old, but the reason I'm replying is that it's been well over two years since K-9 mail has had an update. I ran into this with my old favorite email client, Maildroid, which also has not been updated in more than a couple of years.
Several years ago, my company chose to use Gmail, which is then administered by our "IT" guys. They're called that, anyway. Unfortunately, these administered corporate accounts can't be set up on a phone without installing added software giving the IT guys access to the phone. Additionally, they disabled IMAP, so in a bit of email gymnastics, I have setup a system of forwarding, reply-to's, BCC's, and weird filtering with a secondary account that I can access from my phone.
Short story is, I'm always on the lookout for a superior android client, and am going to use this opportunity to mention that FairEmail, which is fairly new and which I found a couple of months ago, is far and away the most versatile client I've used, ever. Can't say enough good things, and they update what seems like on a daily basis, there have been days where I've received more than one update. It does all the stuff that every other client does, plus a bunch of the crazy stuff that I need it to do, it's pleasant to look at, and it's free, no ads. I bought it just because I appreciate a good app, but if you don't, the most you get is a very unobtrusive line at the top asking you to consider making the purchase if you like it.
Anyway, just throwing that out there.