If for some reason you have to use the camera footage against the dealer for damaging your car, or some other reason, the dealer's attorneys can give you a hard time if they wanted to and it might not even be presentable in court, if you take it that far.
Let's say the footage is uploaded to YouTube, this could be a form of defamation / invasion of privacy.
In court this evidence can be thrown out and you could be counter sued for said invasion of privacy and maybe other legal reasons I am not aware of.
It all boils down to how the dealer handles public relations. Realistically, I think if you leave the dashcam on, or even connected to a large USB backup battery in the glove box, just for your peace of mind, then you will probably be fine. I don't think the footage will help much beyond that. If you do present the footage or even mention you have it to the service advisor as proof of malfeasance, then the dealer can pursue legal action if they want, but this would be extreme. I think you'd have to harm their reputation to get to this point though.
If I owned a repair shop I would certainly have the employees check every vehicle, front and back for cameras, and disconnect them. For "legal and insurance" reasons if anyone asks, I think the dealer has every right to do this or even deny service.
Service contracts should be updated with disclaimers about recording technologies, maybe they already are.