Byobu supports `mail notification':
mail - system mail for the current user; the letter '[M]' is displayed in the lower bar toward the left in black text on a grey background
How could system mail be set to regard IMAP accounts?
You need to configure your system mail client included in the mailutils package to receive mails from you online account (e.g. gmail). Last time I checked the mail notification feature in byobu was premature. See https://answers.launchpad.net/byobu/+question/143784