Is it possible to show a static page if all ELB registered instances are down?

We are using AWS ELB to offload SSL and load balance the incoming traffic. If all instances are down/unhealthy the ELB just sends back a blank page with HTTP status 503.

Is it possible to send a static page, to indicate maintenance, for example?

You have a couple options I can think of:

1. Put AWS's Cloudfront CDN in front of your ELB, and customize the error response for 503 errors. Details on how to do that are in the AWS docs and it can be done via CLI or the Console.
2. Use AWS Route53's (or another DNS provider, if they offer something similar) DNS failover to detect when your ELB is down and point DNS at something else like a backup server or an S3 bucket. Details on that are again in the AWS docs.