The question is often asked about why fiberglass filling is used, and does it reduce the box volume. Does it Reduce Internal Volume? Insulation filling will actually ADD to the effective volume "seen" by the driver. This seems counterintuitive since the insulation takes up space. This exists because of the thermodynamics within the cabinet. An unfilled cabinet is an adiabatic thermodynamic process. When the driver compresses the air, both the pressure and temperature are raised. If you fill the cabinet with fiberglass insulation, the fiberglass will absorb the heat created by the air compression. The thermal mass of the fiberglass keeps the temperature constant. You now have an isothermal system. The equilibrium state is the same with or without compression. Adding the thermal mass (i.e fiberglass insulation) lowers the resonance of the box, so a smaller box can be used to achieve the same resonance. I have never measured and verified this, but some technical papers will claim that you can increase the apparent size of the box by 15% with dacron and up to 18% for fiberglass.
What is the Insulation/Filling For?
The main reason for using insulation in a box is to reduce standing waves. Reflections of sound off walls and features of a box will mix with other waves inside the box. They will add or subtract depending on phase and time delay. A spherical enclosure would be the worst since surfaces are equidistant. A square box has a lot of standing waves. This family of standing waves adds to the sound of the box, especially in the midrange region. You don't want the box creating sounds of its own. The standing waves can also excite resonances of the panels, making additional noise. Some speaker manufacturers add bracing in the cabinet to break up the standing waves. You can completely fill the box with fiberglass if you like. Thiele documented that damping the vent (port) with filling will reduce efficiency, so keep it out of the port if your design has one. Foam products will accomplish suppression of the standing waves if they have acoustical absorption properties, but they will not have the thermal properties like the fiberglass. This is why foam is not recommended.
In summary, the speaker will "think" it is in a slightly bigger box with the insulation. I would recommend assembling your box without the filling first and listen to it. If you are building two boxes, assemble one with and one without. The box without filling will sound louder, but the extra volume is the added coloration caused by the standing waves. I would think one would want to hear the beautiful sound that your instrument created, not sympathetic vibrations, resonances, and nulls of a wooden box.