And if they record to a VHS tape, I might be concerned. Once it hits the MPEG encoder, not so much. The entire point of MPEG is to throw out as much data as possible if it isn't perceptible by humans and recreate it as something that is much smaller but looks the same to human senses.
MPEG is perceptual encoding. The imperceptible would be lost by design, not because they were trying to ensure privacy but simply as a side effect of the design.
Yes, they could easily design cameras that could use stenography to encode data in the mpeg stream that would survive, but that isn't what we're discussing. We're discussing power line noise making its way through the entire system and being used to ID a recordings location.
Even so, assuming an analog recording, I'm still inclined to believe it would rarely work just based on modern electronics having so much built in power supply conversions and filtering. Digital ballasts for example are going to make it hard to see fluctuations in lighting.