But the question here, does Exchange 2007 support the use of wildcard certificates?

Yes it is supported for OWA, ActiveSync, POP3, IMAP and outlook anywhere.

However, Configuring Outlook Anywhere after getting a wildcard certificate always returned the following error when launching Outlook.

If you want to use Outlook Anywhere together with a wildcard certificate, you have to modify your Outlooks Proxy Settings to connect to Exchange.

You will need to change the value of the principal name that proxy servers need to have in their certificate to match the wildcard name of the certificate. See below:

Configuring settings for the Autodiscover service:

When Outlook 2007 clients connect to its Exchange 2007 mailbox, they will use the Autodiscover Service to retrieve all configurations.

You may need to configure Autodiscover, to return the correct information to your Outlook users.  To do this, run the Set-OutlookProvider cmdlet in the Exchange Management Shell on the Client Access server. The Set-OutlookProvider cmdlet changes the CertPrincipalName parameter for the EXPR Outlook Provider.

Set-OutlookProvider -Identity EXPR -CertPrincipalName msstd:*.systems4arab.com