Yes, AppHarbor supports custom hostnames. From support response:
you'll essentially need to set up a CNAME for www.somedomain.com which point to your app on AppHarbor - for instance using the foo.apphb.com URL. If you're in doubt about how to configure a CNAME for your domain name on GoDaddy I'd recommend reaching out to them.
On the AppHarbor end you'll just need to add www.somedomain.com to your "Hostnames" section
More here: