Is it possible to manage Battle.net friends out of game?

There's currently no way to add or manage friends other than via the in-game client.

However, since BattleTag friends are shared with SC2 BattleTag friends, you can see a list of your friends if you visit your SC2 friends page (assuming, of course, that you and your friend both have SC2).

Your SC2 friends page should be at http://<"eu"/"us"/etc.>.battle.net/sc2/<"en"/etc.>/profile/friends (e.g. http://eu.battle.net/sc2/en/profile/friends if you're logged in to your EU SC2 account on Battle.net).

Looking at the real id faq you can only add friends in-game.

Battle.net Desktop App now support chating with friends and you can add new