No. You will lose some of the lowest frequencies because the driver will not have enough "strength" essentially to move slowly against the higher pressure build up in a smaller box. That is the best way I can think to explain it. A smaller box will get a sub to hit quicker and be more "musical" and will not hit as low. This is true for sealed boxes.

Ported boxes are different because you are going to tune them for certain frequencies based on volume and port size.