Bungie had previously announced the PC version for Destiny 2 would be available exclusively on the Blizzard Launcher. With the game being on Blizzard's Launcher, Destiny 2 will maintain the launcher's full functionality, such as the cross-game chat, ease of adding friends, and more. However, because the Destiny 2 will play alongside Blizzard titles like Overwatch, Heroes of the Storm, and World of Warcraft, cross-game items might be available in their future.
Blizzard has, time and again, featured other title's characters or cosmetic items in their other titles. For example, when Heroes of the Storm began the Nexus Challenge, Overwatch players could unlock unique skins for the shooter.
During the GameSpot interview at E3 2017, Bungie's community manager David Dague (better known as DeeJ) stated, "There's certainly no telling where this relationship will bring us in the future, but I don't have any announcements of cross-game promotions or engagements at this time."
Granted, that's no solid confirmation of Blizzard cosmetics making their way into Destiny 2, but they are not shutting down the idea of bringing in Overwatch-themed armor or potentially hidden Easter Eggs in future game content.
Imagine what Blizzard games could port over from Destiny 2. It's not hard to imagine Overwatch's Soldier: 76 in a full set of Hunter armor, or Reinhardt gearing up with Titan pieces or Cabal pieces. Similarly Destiny 2's main boss, Ghaul, could be added as a battle-pet for World of Warcraft.