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Because GW says you can do this now...

Genestealer Cults (Vanguard detachment)
1 Patriarch
1 Primus
3 x 15 Purestrain Genestealers

Tyranids (Spearhead detachment)
1 Winged Hive Tyrant (adrenal glands, 4 deathspitters w/slimer maggots)
1 x 3 Warriors (devourers, adrenal glands)
1 x 30 Termagants (fleshborers, maybe a few spike rifles)
2 x 3 Biovores
1 Carnifex (1 pair talons, 1 pair crushing claws, thresher scythe, adrenal glands)

Astra Militarum (Battalion detachment)
1 Company Commander
1 Commissar
1 Tempestor Prime (Command rod, plasma pistol)
1 Tempestus Command Squad (4 plasma guns)
1 x 5 Scions (2 plasma guns, plasma pistol)
1 x 5 Scions (2 meltaguns, plasma pistol)
1 x 40 conscripts
2 Basilisks

2000 points exactly if my math is correct. Would it work?

I think it might. Whats your plan for Flyers, and Super Heavies?

Patriarch + genestealers and might from beyond can tear up a superheavy in a couple of turns. With three units and a primus reroll I should be able to get at least one 5 or 6 on an ambush roll so I can charge without taking losses. If the scions soften the target up with plasma first then it should at least be crippled after a turn.
"Hard to hit" flyers will be a problem but I don't know if it would be enough to justify taking a hydra or melee flyrant.

Sounds good. I honestly don't know if Flyer spam going to be a "thing" or a flash in the pan yet. Time will tell. Good luck! And good hunting!