Yes and no.
In the current timeline and zone design - that is, since Cataclysm, there are Stormwind troops around Sentinel Hill - but without the (signature) closed helmet shown in the teaser.
The current HS story plays in the past , though, when local “The People’s Militia” tried to fight back against the Defias Brotherhood, as I mentioned before, since Stormwind was unwilling/unable to spare regular troops.
Proof: The Barrens are still one mostly arid zone, not divided by the giant rift valley caused by Deathwing.
Additionally, the mercenarie’s story circles around Varian Wrynn (Anduin’s father) gone missing on a diplomatic journey, which was part of the original WoW lore until he came back to Stormwind and fought Arthas’ Scourge in the Northrend campaign.
Trailer with Deathwing destroying much of old Azeroth, including a signature watchpost in the Barrens:
Team 5 is free to take their liberty with it, of course, as they did before. Hearthstone’s stories aren’t canon WC lore.