No. The ELB has a DNS entry that you can setup on your DNS provider or
on Route 53. This DNS is the only external link to the ELB and ELBs don't
have elastic IPs. Also, keep in mind that the DNS doesn't change on your
ELB but the IP can change at discretion of Amazon.
Also, Amazon uses it's own internal mechanism to access instances behind
load balancer and I'm pretty sure it doesn't use external addresses (most
Another alternative is to setup your own HAproxy instance in EC2 and
configure it with an Elastic IP, but that's a little bit more work. (Also,
you have to monitor it closely as you would have to manage it in case of
changes in traffic patterns)
Hope it helps.