Is it possible to invite others to watch a replay with you?
Not currently possible. But a lot of people have been requesting this feature, and caught Blizzards ear. If/when it actually gets implemented, who knows, but at least there's this:
This is a functionality we're interested in providing our players at some point in the future. :)
http://us.battle.net/sc2/en/forum/topic/189279348#7
You can load the same replay with your friend and start at the same moment and chat. I often do it with my practice partners after the game.