Multiple Availability Zones + AnyCast?

When a second availability zone is added, would it be possible to support AnyCast ? I.e. Having the same IP assigned to multiple servers in different datacenters ?

I think this could make a nice alternative to having to provide load balancers, a low TTL DNS with failover / Geo support and would reduce the number of public IP addresses required.

I am in need of the same process for our QNAP. Has anyone looked into this? Is Dreamhost able to support AnyCast?

If not what is the workaround?