No date on when it will happen.
Mass Effect Andromeda will have a multiplayer beta on consoles though it seems to be more of a closed test instead.
Producer Fernando Melo on Twitter noted the beta and revealed that it would only be for Xbox One and PS4. No date has currently been revealed and you’ll need to sign up for it on Bioware’s Beacon website. Participants will likely be chosen individually though it wouldn’t be strange to see an open beta for all platforms at some point.
The multiplayer will be similar to Mass Effect 3 in that four players will work together in a series of missions. Will they be Horde-style? For now, we know that there will be custom conditions players can enable for increased experience and rewards. Custom missions will also be created by Bioware for Mission Points that can purchase actual equipment rather than relying on the RNG from equipment packs.
Mass Effect Andromeda is out in Spring 2017 for Xbox One, PS4 and PC though there are some indications that it could release on March 21st 2017.