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.
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.