They would've lost at Vraks if space marines (4 different chapters of them) hadn't intervened several times to take important locations and defeat important enemies before leaving to do stuff they considered more important*, not to mention the Inquisition and 22 titans by the end of the war. Indeed, prior to the arrival of the titans and some new regiments as part of a reinforcement wave with a new commander in charge the war was lost, the DK already deployed were cut off, being systematically destroyed and generally just knackered.
Honestly I would probably have taken the Armageddon Steel Legion over the Death Korps for Vraks, though I do prefer the DK aesthetic their tactics are less than stellar even for their supposed speciality given the gear available. The main weakness the DK assaults had was improper use of armour and slow movement speed, as well as an aversion to actual thinking. The Steel Legion uses Chimeras which are fast and heavily armed with good frontal armour and an enclosed compartment, while the DK prefer Gorgon Transports, which are slower and open topped even if more heavily armoured and able to carry more men at a time. Really an open topped transport is a weird thing in general, especially when you still need a door to deploy from it.
A rapid massed mechanised assault of Chimeras and Hellhounds could easily burn out the outer defensive trench lines and better protects the infantry from artillery fire than the gorgon, as well as better able to follow and support disembarked infantry in most terrain. Chimera's are also amphibious vehicles, well suited to function in the muddy terrain of Vraks. I'd probably want some Elysian Drop Troops regiments in a perfect world, but I think Vraks was ill suited to most fliers due to the electrical storms, the DK didn't bring fliers any in any case.
Of course this is a battle where Death Korps regiments tried to retreat. Some even shot their own Commissars for trying to stop the retreat, so I'm not sure any guard force could do it without problems, but I do think some could have made far better progress at it while also being more resistant to the traitor's main arsenal of artillery and massed small arms fire.
Granted the DK are somewhat better suited to resist chemical warfare than the Steel Legion, but considering that the chemical weapon that was stockpiled on Vraks literally melted DK soldiers into skeletons through their jackets and respirators I'm not sure being better at it matters much. Liquified is liquified after all.
*Weird thing about Vraks, it's this super important location, holds a vast amount of weapons, distributes them and serves as a collection point other planets send psykers to so they can be held until a Black Ship arrives, and yet Space Marines generally only got involved when the DK had hit a major blockade, like fortified gates they couldn't take after weeks/months or when a chaos marine warband was actually doing stuff. Similarly despite this planet being so important the Sector Command officers kept considering writing it off and pulling out the forces because they were taking years to make any progress. Hell, it took 17 years to capture one city.
Another, odd thing, according to SoV the Death Korps don't deal well with mud. They train on Krieg itself, which is mostly ruined buildings and metal/concrete trenches from their civil war. Which makes sense, it used to be a Hive World, so actual bare earth is probably in short supply, but it's weird to think of the WW1 themed regiment not being from a muddy wet place.