That’s awesome, the June-60 looks really cool!
Yeah that sounds like it should work, have the output 3.5mm cable from the OP-1 go into the input of the June-60, then you’ll need another 1/4 cable to connect the output of the June-60 to an amp or a speaker of some sort. Unfortunately you wouldn’t be able to have the June-60 work without plugging it into a speaker as the OP-1 doesn’t have an fx loop. But an external speaker sounds much better than the internal OP-1 speaker anyway.
Looks like the June can run off battery as well, or you’ll need a power supply of some sort. Typically battery powered pedals will turn on when a cable is plugged into the input, so if you go the battery route remember to unplug the audio cables so the battery doesn’t run dry on you.
Hope this helps!