I think that all three superweapons should be able to affect it if this was done, assuming it is gray goo, the Novalinth can nuke it out of existence and the deliverance engine can jam the signals holding the swarms together.
Alternatively, it could be made that you could play the campaign as any of the races, over the missions you acquire technologies from the other two races, culminating in both of them giving you their superweapon techs before the last mission, which your scientists combine to make a superuberweapon that nukes a planet, disables/destroys structures/ships in orbit, creates a phase node (supposing Vasari phase nodes can be acquired by the other races), and spreads your culture (supposing the Advent's culture vision can be acquired by the other races.)
In the ending scenarios, you fight delaying actions against the Darkness, trying to stay alive for X amount of time or hold a choke-point planet for so long. The other two races' high commands approve ceasefires during these missions, joining you and allowing you to concentrate on slowing the enemy's advance. Meanwhile, in the core worlds of each faction, scientists race to find a way to combine the Novalinth, Kostura, and Deliverance as I stated above. You are dispatched, as your chosen factions best sector commander, to try to support your allies' core planets but both are overrun despite your best efforts (these are two more delaying action scenarios.)
The survivors are evacuated to your home sector where their scientists combine their efforts with yours as all three fleets prepare for a desperate defense of their last hope of salvation (the last scenario starts with all planets divided evenly between the three factions, all but one of the research items are finished, this tech is called different things for each faction, but all three unlock the superuberweapon, it is only available to human players and is extremely expensive, and takes a half hour to complete.)
The opening attacks of the Darkness are on your allies' planets, when it reaches a pirate base, a cinematic shows the base being captured. A message comes from the pirate factions (who have been conducting their usual raids) pledging allegiance to your empire while the pirates appear on the diplomacy screen as "Allied" with you and both visions. The remaining pirate bases on the map are emptied of ships as the pirate fleets move to bolster the crumbling defensive forces of your allies.
As the darkness breaks through your allies and starts assaulting your worlds, you finish research for the weapon, which is constructed like a starbase. You build some and start blasting away at infected worlds. As they are cleansed, you move in weapon constructors to increase your firepower, of course, you must move ships up with them, because once a Novalinth-esque timer expires, they are able to be recolonized by the Darkness (and you can't colonize any planet that has been under Darkness control). The end objective of the mission is to defeat the Darkness. An ending movie shows your empire establishing a defensive perimeter to hold back the Darkness, and destroying/subjugating the remnants of the other two (I don't share your optimistic hope that the shared enemy will cause them to permanently ally, plus, if your going to make a franchise killer, make it so you can't do what Pirates of the Caribbean did and try to keep going)