But, you are basing this statement on a mere possibility that is running around in my head. I have absolutely no fact to base the likelihood of this possibility coming to pass. I have used supplemental lighting successfully every year for the past 4 years, without a single issue with a broody. Typically, I start my lighting in November. In October, I had to break 2 broodies. This was based on completely natural lighting, with diminishing day length, and sub freezing weather. So... to say that supplemental lighting causes broodiness out of season is an erroneous statement.
One could also come up with the thought process: "keeping day length consistent, also keeps hormonal levels on an even keel. So, supplemental lighting is apt to prevent the hormonal shifts that occur in a naturally decreasing/increasing day length." And, those hormonal shifts should be what drives broodiness.