This has been disproved for close to ten years empirically and academically[1]. Route flaps generally result in convergence to the exact same destination if it has another path and is still online. If it's offline, then it's working as intended, and that's no different from a server being rotated via a DNS pool going down.
1: Quick search: https://www.google.com/search?q=tcp+anycast+paper&ie=utf-8&o...