Depends on the configuration, but most likely yes. The reason being that your custom domain will have a MX record which points to the blocked email provider.

• If the MX points to a domain and the domain is already blocked it will stop there.
• If the MX points to a domain and the IP is blocked, it will resolve the domain, see the IP of your provider and stops there.
• If the MX points to a IP and the IP is blocked, it stops there.
• If the MX points to an IP and only the domain would be blocked, it might go through … unless they also check the reverse DNS entry, which may show the domain and thus will block it as well.