We do compression in PGP.
Does this step increase/decrease or either have any effect regarding the authentication of a message?
From RFC 4880 - Open PGP Message Format (emphasis added)
OpenPGP implementations SHOULD compress the message after applying the signature but before encryption.
As the signature provides authentication, and you specifically ask about authentication, I think that quote from the RFC should answer your question. Compression does not affect authentication of the message at all as the authentication step (signing) is applied before compression. See the question archie linked for other issues with compression.