Will an airliner with a quieter cabin have a quieter cargo hold?
The cargo hold will probably be quieter if the cabin is quieter, but there are multiple variables that can affect this. As Peter Kämpf commented, the noise source will depend on the position in the airplane. The two main sources of noise are the air moving past the airplane, and the engines. The two main noise concerns of manufacturers and operators are cabin noise and community noise.

Reducing the noise at the source is one option. Engines are the main sources of noise and receive special treatment to reduce noise as much as possible. This can reduce cabin noise and/or community noise, and should help both the passenger and cargo decks. Newer aircraft like the A380 will tend to have quieter engine installations than older aircraft like the 747-400.

In the case of the cabin, noise can also be controlled with insulation. Insulation in the cabin will help with both noise and temperature control. Both are less important in the cargo hold, but do have some importance since it is only separated from the passenger area by the floor. Cargo hold insulation will provide protection for structure from fire or accidental damage, and some degree of temperature protection. So it is possible that the cabin receives added protection from these features that the cargo area does not benefit from.