A large cage probably doesn’t need to be grounded to prevent a relatively weak signal from escaping, as attenuation would be high due to the amount of material involved. Smaller cages may radiate the signal after some attenuation.

Edit: reading some more about it, cages that are close to the radiating element may experience capacitive coupling, and this is what can cause an ungrounded cage to serve as an antenna. A larger cage, with the radiating element farther away from the cage, is less likely to experience this. In either case grounding should reduce this risk.