It's sort of an interesting idea. I seem to recall that, in the elder days, they often had Genestealer Cults fail to achieve their endgame, and instead turn to Chaos. The "mainline" Tyranids, though, I don't think they could. One of the things Chaos needs is your soul, and most Nids don't seem like they would have one. Wanton destruction is nice, but that's not Chaos's big goal, or the Dark Mechanicus could crank out a vast army of robots, and just wreck everything. Also, one would have to break synapse control to get tainted in a controllable way, and I see the Tyranids as being able to tell. A race that often tosses itself into acid, so that everything it harvested on a world can get sucked back up, into the bioship, and then reformed again, if need be, could probably sense those stragglers who are no longer "like them", and they'd eat them, like a virus in your body. Whatever the Hive Mind is, it appears to be very powerful, and I don't think that any "lesser" Chaos angle could corrupt its hold; maybe Tzeentch, himself, but that's a bit more direct than they are known for.
That isn't to say I don't like your idea; it's just that GW seemed to like to be sure that the whole universe was Us against Them, and/or Us against Us, with us bein Humanity. If Chaos could ever be bothered to pick on another race, Humans might get too much recovery time. Orks and Nids have a built-in "free from Chaos" tag, even if thhey might seem like Khorne and Nurgle personified, respectively, as do Necrons. The Eldar and Dark Eldar take radical pains to avoid it, and the Tau are vaguely either immune, resistant, or unknown to Chaos. That mostly leaves just Humanity for Chaos to bother, just so the future stays grim and dark. Certainly, other races do, or have done stuff with Chaos, but we've killed many of them.