I'm not sure how it works through steam, because I don't launch the game through it. Either way, your update will not be effected by the servers going down unless they take the update servers down. PS: While steam has it's bad moments, it's still better than distribution platforms like Origin or uplay.
I understand the rush to play, but execute some patience. Launch days of expansions in any game is always chaos and huge server issues, not just free to play games.