Does the operator have to square the work piece to the gantry with every setup?
The simple answer is yes, you need to place the work so that it is square to the machine, if the part is already cut to size.

I'm used to working with machines with pop up pins, so I work in a similar fashion. I have a permanent X and Y fence on my machine, that is machined after homing the machine. So all I do is turn on the machine, home it, and place the part in the corner against the fence, and it's ready to go. Similar to what Biggs does.