Is it possible to exclude a specific mailbox from the "Inbox" view in Mail.app?
I got 3 mailboxes in mail.app, 2 of them are mail accounts for normal mail communication, 1 is used for receiving mails from senders which sometimes send to much mail (newsletters etc.). The problem that occurs is that all the newsletter mails show up in the "Inbox" view preventing me to see the mails from the other mailboxes.
In Mail preferences, you can choose Accounts in the preferences toolbar, select the email account associated with the newsletters, choose the Advanced tab, and uncheck the "Enable this account" checkbox. You will need to save the changes in order for this to take effect.
I tested this in Mail on Lion with one of my three mail accounts. Mail removed the account from its mailboxes list; the messages were gone from the unified Inbox, but the account settings remained and I was able to bring the account back just by checking "Enable this account" again.
I don't know of any way to exclude a mailbox from the Inbox view, but you could make a rule in Preferences to move all messages sent to that inbox to a specific folder. Messages to that inbox will appear for a moment when they arrive, then move to the folder when the rule fires, usually less than a second later.
In my iPhone 6+ instance of Inbox disappearing, I found an Edit key above the mailboxes and clicked on it. Up popped the lineup showing Inbox had a button not selected while all the others were selected. I clicked that button on for Inbox, said finished, and there was my Inbox all back into view.
I knew it was still around because I could move a trash item back into the Inbox.
There was a simpler solution here than I had expected.