Yea, I think so. Anything with Pink, Pixt, Pix, Pin with endings -ston, -stone, -ton, -erton, etc. tend to be related I believe. Though it's hard to know because some arose independently and some were misspellings.
Yea, it's been a thing I've wondered about because a lot of my dad's side were in the military / police. Probably just a coincidence unless we all grew up hearing Pinkerton stories.
With the Homestead Riot history, you can imagine having this surname in Pittsburgh haha.