I don´t think Darktide will feature a Cover-System.
Mostly because it wouldn´t make sense in a horde game.
While Fatshark said there will be more shooting in Darktide, it will still be at least 50% melee (since Warhammer 40k is also known for its brutal melee combat, Bayonetcharges/Trenchwarfare etc. are still very much a thing.) or at least I hope for at least 50% melee.
Which would mean, and you can also observe that in the gameplay trailer, that even if enemies shoot at you, you still will get rushed by the horde. So I would argue, it makes little sense to take cover since the enemy will come to you anyway.
What would make more sense is to play like you have an Ironbraker with Drakegun or an Outcast Engineer with Crankgun, (or even Waystalker/Sienna) what I mean by that is → If you have a Character that has a gun which can kill the shooting enemies reliable or better than all the other guns, the other 3 Character can cover him/give him (or her whatever) space. That would mean a bit deeper tactical gameplay.
You can see this now on Maps with Beastmen, it is always smart when there are multiple archers (since they have the accuracy of an Elfen-Sharpshooter at least on Cata) that one/two players clear them out as fast as possible while the others provide cover from the horde/random enemies.
If we are provided cover, would the enemies use it in turn? if they have secured the room before us, or during their advance (maybe only a certain special/elite uses cover).
Now this could work, since we then would have to use Flamethrowers or Grenades to flush the enemies out. Since the players are not a horde, we can not rush like the horde. Would be fun.
And lastly, will cover be destructible, by gun fire or explosives or boss/elite attacks?
Depends on the Engine Fatshark uses, but I don´t think we can expect Frostbite-Levels (Battlefield) of Destruction. But if there is cover for Enemies to use, that would be a good feature, in Inquistor Martyr (Diablo-Like 40k Game) that worked rather well.
But I think we will have to wait until Autumn for the next Gameplay reveals, before that everything is ofc speculation/opinion.