I believe the truly concerned/paranoid will not want to take their car to the dealership for updates at all. Which would, IMHO, be a mistake: having known security holes in your car's software is more likely to lead to a privacy invasion (via getting your car hacked at some point) than letting the dealership get their hands on it for a few hours.
(I should note that all of this is theoretical for me: I drive a car that's old enough it doesn't have any software).
EDIT to add this P.S.: Actually, I can think of one category of people who would be concerned enough to turn off the car's ability to connect to the Internet, but feel fine about taking it to a dealer for updates. That would be people who want to turn off the car's Internet connectivity not because of privacy concerns, but because they don't want anyone to be able to disable the car (either via hacking or via "legitimate" means, i.e. the manufacturer does it) while they're driving. Such a person would care a lot about the car's Internet access being completely off while they are driving, but not care about it being turned on while it is at the dealership.