every Faraday cage I ever worked in was indeed earthed. And to a pretty rigorous standard too.
Depends how you want to use them. The Jet Provost T3 & T4 had fibreglass wingtip fuel tanks. After a couple of years' service, one aircraft had a lightning strike on a tip tank, with spectacular (though fortunately not terminal) results. All the tip tanks were then fitted with fairly crude Faraday cages, just metal straps around and along the tanks termintating in a fitting at the back end for tightening the whole assembly. It worked, though clearly not earthed.