I've got the original Beseler 23c, and can just barely print a 6x6 on 5x7 paper w/ my 105 lens. It's right at the edge of what's possible. It's been a while, but I seem to remember bringing the bellows to full extension and then having to work back and forth between the focus and elevation knob. Several of my prints have the rebate, so there must be at least a tiny bit of wiggle room... but it's a close thing. If the bellows on the 23cII are even a tiny bit shorter, then you'd need that extension....
Actually, I just looked and I think it was my 6x9's that were at the edge. When I print 6x9 ( or 35mm ) I leave a little strip along the top and bottom, so it's even less enlarged than a 6x6. Anyway, I've successfully printed 6x6 and 6x9 on 5x7 paper, for what it's worth.