I thought that THE gate was sealed at the end of MoM, denying the Emperor any chance of fullfilling his project?
So Vulkan's there to ultimately have no impact on the plot. Because a fourth Primarch on the walls wouldn't be a useful force multiplier in every scenario that the Siege throws up...
The Gate is about as sealed as the walls of the Imperial Palace are impregnable. The Gate will come under siege, and pretty much has been since it's closure. Vulkan is there to hold it shut when the assault ramps up while the Emperor and his Custodian Guard are busy elsewhere - at this point, I'd expect a big climax for Vulkan at the height of the Siege, when the Emperor is preparing to engage Horus aboard the Vengeful Spirit. Combine it with Malcador's sacrifice, sitting on the Golden Throne until the Emperor's return, and you've got some big potential for both Malcador and Vulkan to struggle against the predators of the warp in the Imperial Dungeon. And remember that Magnus is back in the game now, too, and the last information he has to go on is that his final shard is somewhere in said Dungeon, and likely ignorant of Malcador's veil around Titan and, by extension, Ianius.
If by "ultimately having no impact on the plot" you mean that "they succeeded in their role, thus maintaining the status quo we remember", then sure, he didn't have any impact on the plot. Vulkan does not have to be an active combatant on the walls to make a difference to the war effort - and it is a war being waged on multiple fronts.
From the old Collected Visions:
The star of the Emperor gave the defenders respite enough that many were able to cross through the portal and retreat into the Imperial Palace. At first all of the tech-priests and workers were evacuated and then, reluctantly, the Silent Sisterhood and the Custodian Guard withdrew from the battle and into the Palace dungeons.
The gate would remain closed to the daemons for as long as the Emperor was able to power it from his throne atop the golden portal. Only the mightiest of psykers had power enough to do this and even then most would be exhausted and fail in a short time. Only the Emperor had the might to keep the gate closed permanently and for him the effort got harder as the daemonic forces gathered about him. For as long as the daemon horde threatened to breach the portal, the Golden Throne would be his prison.
Even just the switch between Emperor and Malcador on top of the Throne would be enough to weaken the defences sufficiently to give Vulkan something to do, I'd say. And seeing how, while Mal is the most powerful psyker on Terra besides the Emperor, he is the weaker one. He will struggle harder than the Emperor did, and in the end it'll likely be Vulkan who picks up the pieces that physically breach the portal, while Malcador is fighting on the psychic level.