you could yes, but the frequency response of the woofer would change, so would its power handling and how it actually sounds.
That is not "free air" (technically i suppose you could call it that) its called open baffle. The mdf would be separating the front wave from the back wave and thus you can hear it. There are many issues involved in getting speakers to sound good in this design, and there are some pitfalls in the design mainly mid-bass output and acutal SPL output with a given input. aka it will be louder in a sealed box with the same amount of power.
It is not suggested if the woofer is not designed/acceptable parameters for it. but it can be done.