If it's one of Bill's chops, he's created swell pedal insert electronics to simulate the tonal change of the original organ swell (e.g the increase of brightness with volume). However, I believe you're right relative to the overdrive part of the equation.
On the chop I built, I have a clutch cable that runs from the swell box lever to the pedal, with a modified XLR for quick connect/disconnect. But I've been tempted to have Bill add his swell circuit to my organ as an alternative solution. Bill also has an effects loop mod which can be used to insert reverb, EQ, overdrive, etc. between the organ preamp and the Leslie.