Is it valid for Jumu'ah prayer to be offered silently, and under what circumstances would that be the case?

There is no situation in Islamic law where the Friday prayer (Jumu'ah) is performed secretly, because it is established from the actions of the Prophet (peace be upon him) and his Companions that the recitation therein is to be audible. The majority of scholars hold that audibility in its proper place is a Sunnah (definition) (recommended practice) or mustahabb (desirable). Imam al-Shafi'i disliked for one to recite silently where audibility is required, or audibly where silence is required, but there is no re-performance of the prayer or prostration of forgetfulness (sujood al-sahw) required of him. As for audibility in the two sermons, it is a pillar, because their purpose is to guide and admonish the people.