It seems that Blizzard is thinking about cross platform play for Overwatch, but not between PC and consoles.
Blizzard seems to be looking into cross-platform play for the console versions of Overwatch. On June 4, 2016, the Overwatch Twitter published this tweet:
It seems to hint that cross-platform play could be a feature for Overwatch in the future. However, there are no plans to implement PC and console cross platforming, due to balancing issues.
Cross-platforming is becoming an increasingly popular feature and topic, especially since Microsoft has opened up to the possibility of cross-platform play between Xbox and PS4.
Cross-platform play would be a overall good feature to have for console games, since it will allow friends with different consoles to play together without spending more money to buy the same consoles.
Rocket League is one of the first games to support cross platform play between PC and consoles, and has been successful in doing so. If Blizzard decides to do cross-platforming for Overwatch, it may be a while until this feature is implemented, but the prospect of it is exciting.