Actually not even close to true for chickens. The Red Junglefowl, the species that gave rise to the domesticated chicken, is classified as Least Concern. As is the Grey Junglefowl, the Sri Lankan Junglefowl, and the Green Junglefowl that contributed to the gene pool. If you're talking about Gallus gallus domesticus itself, then I think that gets a fair bit murkier as they never did survive on their own in the wild. However, with a population of 26.5 Billion in 2023, I think it would take a lot for them to go extinct, and it certainly wouldn't happen overnight. It really varies in my opinion. Obviously types* bred for meat consumption or cage eggs are going to struggle to survive on their own. But I have a Bantum hen that looks and acts like a Junglefowl, being able to clear fly over a 6ft tall person. She's able to nest up high for the night, and is near impossible to catch. I strongly believe she'd manage to survive in the wild quite easily.