You should not use a wildcard certificate for RADIUS. You will need to request a standard SSL certificate.
Once you do that, since clients are configured to not validate the cert ( not recommended), the clients should still be able to authenticate successfully.
Also, it sounds like you are referring to the informational box that pops up asking you trust the certificate? Using a public certificate will not stop this message. This is a normal part of EAP-PEAP. The only way for that message to not appear during the first connection is to preconfigure your clients using something like Group Policy, Profile Manager, MDM, QuickConnect, etc.