The big reveal in ROTJ when we see his face up until that point he had medical droids maintaining his appearance. I don't reckon anyone else would dare to confront Vader looking the way that he did. The reputation of always being on duty and being with the stormtroopers would also remove him from constant interaction with the offices yet we did see briefly in the ESB he was witnessed without his Helmut so what is the likelihood that a snr Admiral caught a glimpse of Vader's disfigured face.
Piett seemed repulsed in Empire, indicating that he had probably never seen Vader without his helmet before.
I took it more as a mixture of repulsion and curiosity from Peitt(and even then he only see's the back of his head) which definitely suggested to be Vader's appearance was not at all well known.
It seems that by time of TESB he stopped giving a crap whether or not imperials would see him without it. So I'd guess that yes, some people saw him without the helmet. Definitely Cylo and other phycisians who took care of his physical wellbeing.
I thought Piett was more surprised. Most likely he was thinking, Huh, so that's what he looks like without that helmet... But Vader only took his helmet and mask off when in his specialized chamber, or in the care of the medical droids/techs. While he wouldn't care if anyone else saw him without the mask/helmet, I doubt most ever had that opportunity to see him sans the mask/helmet.
Without the helmet they would know he was Anakin Skywalker or perhaps his appearance was so distorted and Skywalker had not been around for decades that Piett and others would be unable to draw a link between Vader and Anakin. Vader came along the same time Anakin went missing so the typical Imperial officer sees Vader as having killed Anakin and Obi Wan since he also went missing at the same time. Vader wears the mask to keep a perfect secret remaining an enigma. Nobody is truly sure where he came from, the Empire by comparison well known by the populace and snr ranking Imperial officers so no need to deceive them into where he came from. He governed through terror and you notice none of his moffs or Grandmoffs wear any masks.
In canon, just medical droids/attendants, Palpatine, and Luke. In Legends, Galen Marek saw him unmasked as well and I also think he was battle-damaged shortly after ROTS in some comic.
