The Tyranids have evolved the perfect defence against the corrupting powers of Chaos, if an individual Tyranid is tainted the others kill and eat it. The warp is a psychic force that affects the minds of those it corrupts even Nurgle's diseases are as much a neurosis as a physical contagion. So by killing the individual the collective can cleanse itself of any Chaos taint and it can keep doing this as long as it has sufficient energy/biomass to work with.
Which is not to say the Tyranids are completely immune to the forces of Chaos, if a hive fleet entered the Eye of Terror it could be corrupted so much so quickly that the hive mind would be unable to maintain control. But that would just be the loss of one hive fleet, if that fleet left the Eye of Terror other Tyranid fleets would intercept and consume it, doing exactly what they would do with a corrupted individual just on a larger scale.
Of course the Tyranids wouldn't enter the Eye of Terror or the warp in the first place because they're well aware of what would happen, it would be like sticking you arm in a septic tank why would you do that to yourself?
Suffice to say the Choas gods have no sway over the Tyranid hive mind although they may be able to communicate with it directly and it with them, but I can't imagine either would have much to say to the other. There's simply nothing the Choas gods have that the Tyranids want and any attempt to corrupt or deceive the hive mind is futile, it's probably as smart if not smarter than a Chaos god but only cares about eating and evolving.
Or I could be wrong and it has discussions about the nuanced details of tentacle hentai with Tzeentch and Slaanesh, that are beyond the comprehension of mere mortals.