Hi Carl,
It's not a great idea because it potentially limits the performance the sub will be capable of. The EP350 is an extremely capable subwoofer and it deserves to be ideally positioned in the room.
You could always try it, of course; you might get lucky. On the other hand, I worry about the surrounding cabinetry and the potential coloration that might result. As others have noted, subwoofers radiate in all directions below about 80 Hz and are designed to be operated more or less in free space. The cabinet interference might do unpredictable things. The sub also may cause the cabinet you are building to resonate at various frequencies.
Regards,
Alan
