I'd be still concerned for mid level boxiness in here. It could be difficult to hear, but you MAY get some resonance from the box at certain frequencies. Would be interested to set a speaker up in front of it and hit it with a sine sweep and listen for anything weird going on. The size of this box means that if there IS some resonance, it'll be fairly high. Ran a quick room mode calc on it. Be wary of the 300-500Hz region. On the other hand, it may not be noticeable. Time will tell. Just something to be wary of and listen for.
I would personally move to actually make the unit more breathable. If it doesn't have enough insulation to hit the lower frequencies, boxing it up like that might contain new ones from your voice. Thus creating more problems. Conversely, you may block out the low/mid room frequencies as well and they may be more significant. In an ideal world, it's probably a matter of finding the right balance. I'd take a guess that those perforated holes in the commercially available units are there for that purpose.
I'll be interested to hear how it all goes.