Actually it looks like a bug. Because if you receive an email while KMail is not minimized, trigger a notification once, then when you minimize you are notified of further new mails.

But I succeeded in not being notified in the following ( weird ) way:
- Start KMail, send an email to yourself.
- Close KMail before you receive the mail.
- Restart KMail and minimize before you receive the mail.

Then, you receive your email silently ( the unread mail counter is incremented though ) I said that this way is weird, because when I sent the email not from within KMail but from the webmail interface of my IMAP server, I was still notified.

So welcome to the riddle of notifications:)

( If you try to reproduce this situation, maybe it is important that I mention my full setup: I am running dovecot IMAP server locally, and the emails are fetched from a few accounts by fetchmail and piped into procmail. Procmail dispatches emails whose senders are me directly into my Sent folder. The webmail interface I mentioned above is the interface for one of the IMAP accounts from whom fetchmail fetches )

"But I succeeded in not being notified in the following ( weird ) way:
- Start KMail, send an email to yourself.
- Close KMail before you receive the mail.
- Restart KMail and minimize before you receive the mail. "

Yes than I get a notification. But the problem is not only the notification: Kmail does not check for mail if it is minimized. 

>Kmail does not check for mail if it is minimized.

That problem I didn't come across, minimized or unminimized it always checks for new email. If you have the opportunity, could you try a later version and see if that one works? Checking your KMail configuration may also be helpful.

PS: Now I felt bad because by changing the summary I sort of stole your bug report:) If you like I can open another one and revert your summary to the original.