I found out by accident that there IS a draw.
I'd been dragging my toad around for 2 years. Starting it every 250 miles per instructions to cycle trans fluid.
Then on my last trip to Florida I due for the 250 mile stop and run but was so close to my destination that I thought it would not hurt to go the extra miles without stopping to start the toad. So I skipped it.
Had a dead battery when I got there. Apparently me starting the car for the trans every 250 was ALSO charging the toad battery. :S
So it does depend on how your toad was wired.