I have the 27683, and the only reason I can see for having that pin (other than being a PIA to align!) is for the fixed base. I suppose that if the motor is allowed to rotate, the coarse adjustment tab (that fits into one of the three horizontal slots on the motor housing) might slip out, letting the motor slip. I gather, though, that the fixed base does have the pin in place.
I don't see any reason when using the plunge base. The motor slides down until it seats fully into the base.
Perhaps the reason is as something of a safety factor- if you forget to clamp down the motor before turning on, you could end up with some nasty, unexpected rotation
I'd say try using the router without the pin, but make sure that the little black triangle markings line up as much as possible, and ALWAYS clamp the motor before turning on!
Whenever looking at tools at Sears, I'm always amazed at what would-be customers do to display models, but wonder how or why that pin could be removed.
BTW, if you haven't found it already, you can download a pdf of the user manual by going to the Sears Parts Direct web site, click on the "Manuals and Repair Help" tab, and enter the model number (including the 320). Good luck. I've been very happy with my 27683.