This is a partial answer/guess to my question, but I hope if someone else comes to this question, they are able to benefit from the answer.

The workaround is to configure Full Text to not verify signatures. This is accomplished by executing the following SQL Command:

EXEC sp_fulltext_service 'verify_signature', 0;
GO

Based on the above setting of not verifying signatures, I found the following page: https://msdn.microsoft.com/en-us/library/ms142595%28v=sql.90%29.aspx

This pages indicates that the filters used by the Full Text search need to be signed, which would explain why an error involving certificates could be generated when creating a Full Text database.

This pages provides a map of the components that make up the Full Text search architecture, provides some insight into the executable or *.dll files that may need to signed: https://technet.microsoft.com/en-us/library/ms142541%28v=sql.90%29.aspx

The error in the question references the "revocation process". On the computer that is producing the error, another application displayed an error in it's certificate properties window that said:
Windows cannot determine the validity of this certificate because it cannot locate a valid certificate revocation list from one or more of the certification authorities in the certification path.

The computer producing the error does not have access to the internet, which prevents the OS/certificate management software from being able to validate the revocation lists.

So the 'guess' about what is happening is that when the Full Text database is created, one step in the database creation process is to validate the signatures of the filters used by the Full Text search. Part of the validation of the signatures includes validating the revocation list, but this cannot be completed because the computer is not on the internet, which results in the production of the error.

I hope this helps someone.

This may or may not help future users, but I was able to fix the
'The revocation process could not continue - the certificate(s) could not be checked.'

issue by making a change to the STATE registry file. However, the installers I was was trying to run would get this error when trying to install Windows Updates with an offline installer.

Open REGEDIT.exe and change STATE from 1000 to 23c00 in:

HKEY_CURRENT_USER\SOFTWARE\MICROSOFT\WINDOWS\CURRENTVERION\WINTRUST\TRUSTPROVIDERS\SOFTWAREPUBLISHING\STATE

You are looking for the WinTrust folder which may or may not be in currentversion.