Yeah, the way the OC-2 works is that it creates that square wave that's an octave or 2 octaves below the input, then uses the octave square wave to cut the input signal on and off. So in normal functioning, you're not meant to ever hear the square itself, which is why there's no gate circuitry there.
I honestly don't know if there's room in the Boss enclosure for the gate, as I built mine in a Hammond box. It's possible to build a pretty small gate circuit that would do the job - you don't need full envelope following, just an on/off affair.
The real fun starts when you use the octave down square wave as the carrier in a ring modulator...
