Nope. If I try to add an outlook.com account I get the same "admin requires your device to be managed" message.
If I try to manually add it with IMAP it tells me "Logins are disabled for "Largecorp"
There are some email apps on Android which 'sandbox' the accounts to get around required permissions, I use BlueMail. There may be a similar app in the Apple ecosphere though I'm afraid I don't use any Apple products so can't make a specific recommendation
Ha ha....ha
Rather than using outlook for IOS can you setup an office 365 account and have email show up in mail (and calendar invites shown up in calendar)?