Blizzard has said that cross-play is something the team is still considering for Overwatch. The game has been announced for Nintendo Switch and will be available next month. Blizzard says that they are not sure at present that cross-play is something that makes sense for Overwatch and is looking at how the technology develops before making the commitment.
"Cross-play won’t be available at launch. Blizzard sent the following statement to Engadget regarding cross-platform capabilities: “We’ve seen how compelling cross-system play can be for our community, and we’re excited about the potential. There’s still a lot of work to do on both our side and the platforms’ side to determine whether this is something that makes sense for Overwatch, and we’re keeping an eye on how cross-play systems and technology develop.”