Hi,
Yes, true the certificate doesn't support the your CRM Server's FQDN. If its a wild card certificate make sure your certificate domain and your internal domain are same.
If both are same then there will be no issues, if both are different then you will have authentication issues.
While configuring the IFD from Deployment manager we change the settings and bindings to your internal one.
When we install the CRM you can access CRM using FQDN name, but once you configure the IFD then you need to access the CRM with Internal or External URL's.
Regards,
Khaja Mohiddin
http://www.dynamicsexchange.com
http://about.me/KhajaMohiddin