I got the Samsung/Seagate 2TB drive for my first PS4 about a year ago. It was the cheaper external USB one where I pried open the case to put it in the PS4. It chirped incessantly, even during games. Even though the chirps were relatively quiet, it was happening way too often. So I returned it for a bare version of the same drive. The bare one chirps only when it's on the PS4's menu and not too often. It was easy to get used to.
I read a theory that the chirping is indeed related to power-saving. Some people thought the chirping occurs when the drive is parking its head. Though you would probably hear it happening when used in the USB enclosure, and I don't remember it happening when I first tested it. Anyway, the interesting thing is that some people think the external version might be configured to go with lower power, thus the higher occurrence of beeps. Regardless of whether this is true, I would caution people thinking about saving money and going with the external version they can pry open.
As a note, I got a second PS4 about a month ago. Bought another bare version of the drive--supposedly a newer version than the one I got a year ago though the model is the same. It doesn't chirp at all. Fingers crossed that it doesn't start happening!