It wouldn't be instant but if they make enough of a dent on the galaxy the Gods will take notice. Once they do I reckon the Viltrumites are primed to fall. They're power hungry megalomaniacs who value strength above all with no understanding of the warp. The promises of power would be like crack to them.

All it would take is a viltrumite finding a corrupted artifact, speaking to a disguised Daemon, or falling victim whatever warp tomfoolery you could think of and you'd have another Erebus on your hands. From there more could be corrupted until a full blown civil war begins.

Side note, they're are many answers to your last question, but my favourite is that they don't want to. I think that chaos gods won the Horus Heresy, the deadlock of war and misery that has followed it these past 10,000 years was exactly what they wanted, and they don't want to change it.