It's actually not that hard to add a simple man page if anyone wants to do it. It looks like it's just a matter of adding the man page at debian/manpages/add-apt-repository.1. I've already done this for another command in the software-properties package which also doesn't have a man page (software-properties-gtk, see bug #290308) so I should be able to attempt this once I get some free time. But if anyone else wants to they can try to write their own man page in the mean time and post the patch here.
It's actually not that hard to add a simple man page if anyone wants to do it. It looks like it's just a matter of adding the man page at debian/ manpages/ add-apt- repository. 1. I've already done this for another command in the software-properties package which also doesn't have a man page (software- properties- gtk, see bug #290308) so I should be able to attempt this once I get some free time. But if anyone else wants to they can try to write their own man page in the mean time and post the patch here.