There's different theories on the sub's ability to integrate in that position... I read you'd have to put the sub out of phase if it were that close but then read more... and that was all hooey. It all depends and there's no way to know how it's going to sound without building it.
So, give it a shot... maybe cut a hole and put a built sub into and see how it sounds. I think something that cheap and light will cause problems, though. Maybe mass-load it to the max of its capabilities... rocks, lead, etc. You may need additional bracing/support... nothing major, but you'll have to try it and be the judge on the sound quality.
I think it's a good thought but may be tough to integrate. Let us know... BTW, how'd the balance power/power conditioner thing go? Any improvements?
-C