No. The air volume is a factor in the calculation of the resonance point of the partition. Reducing the air volume will raise the resonance frequency of the wall, and in any event 703 is too dense.
We want the resonance point as low as possible in the walls and ceiling. The lower it is, the lower the frequencies we're isolating. That's an admittedly broad statement, but a good rule of thumb.
Assuming the system is decoupled, the two factors that define the resonance point is the mas and the air cavity volume. Mass is a much bigger driver, so a smaller air cavity is more than offset by an increase in the mass.
The foundation wall, due to the mass of the foundation, will tend to define a pretty low resonance point, so if you were needing closer clearance on the foundation walls, I'd consider using clips and channels and attach to wood furring secured to the foundation.