I think you -could- make some sort of Co-Op 40k game (maybe not a LCG, but still....).
The problem is that you either sacrifice theme ("and the Eldar and Tyranids teamed up against Chaos and the Necrons" at the extreme end) or you sacrifice options ("everybody has to pick one of the following factions, since the foe is X").
I rather like that Conquest actually allows for some alliances between the factions, and it would seem to me that it wouldn't be hard to construct some sort of "team versus team" scenarios, where four or more (or three or more) players choose sides and build single faction forces allied along teams.
As for Necrons and Tyranids.... I see the Imperial Guard maybe joining the Tyranids (with some Genestealer Cult cards added to their mix), and Necrons going it alone. Eventually, as the line developes, I expect to see solo faction play as being more viable (hopefully neither ideal nor worthless however). At that point a solo Tyranid or Necron (or Chaos or Ork or Space Marine) force could hit the table.