Lucky you getting to play theatre organ.
However I thought that the 'stops' on a pipe organ were either fully on or off? Whereas drawbars, even graphical representations of them, also allow the level of each footage to be controlled depending on how far they are 'drawn' out. This in theory gives a huge number of combinations of the eight drawbars.
The basic sounds from each drawbar on a modern electronic keyboard attempt to emulate earlier electronic instruments, and there are no prizes for guessing which manufacturer's sounds they try to match. So the drawbars can be set up in exactly the same way as they were on classic recordings, if you know the settings. There are plenty of settings available on the internet.
However, as Gloria pointed out, there is a lot more to recreating the 'Hammond sound' than simply copying the drawbar settings. I suspect that most people have heard Hammond and other makes, through a Leslie cabinet of one kind or another, and this is probably a significant, if not the most significant part of the 'Hammond sound'. I am not a 'purist' but to my ears, most of the attempts to emulate the complex sound of a 'miked' Leslie electronically are not very convincing. There is an external processor called a Ventilator which would satisfy me, but I'm sure that 'purists' would mock it.
So whilst the 710 and other keyboards allow you to set the drawbars to the same combinations as a Hammond, does it sound like a Hammond? Many people would say not, although that doesn't mean that the sound is unpleasant or unusable. People sometimes seem overly intent on trying to emulate the original as closely as possible. For some, nothing will ever equal the original.
In that sense it is exactly the same with Gloria's Baldwin.