Do all remastered vocals in vinyl albums have been 'corrected" with auto tune?

I would compare an original release to the "remastered" version and that should help to answer that question.

I will say that, back in the day, vocalists couldn't necessarily rely on electronics to enhance/fix their vocals, whether that was during live performances or in the studio. This forced them to train their voices and to also sing with their natural voice.

A good illustration of this is the "Live at the BBC" series from the early 70's.

Check out Elton John, Neil Young, James Taylor or Joni Mitchell. It is amazing how the vocals are every bit as precise as the albums.

Seek out used originals. For the most part, they just sound better– more musical, inner-detailed, and nuanced with superior timbre and color.

Auto-Tune is a brand of software developed by Antares Audio Technologies, yet it the word is always used to mean, "digital pitch correction software," which is like referring to your vacuum as "a Hoover." 

It was made in the '90s to allow easy fixes to slightly off-pitch vocal takes. It became very famous when Cher's '97 hit single, "Believe," employed it for a different purpose, a distortion of the vocal to give it that digital warble-warble sound. 

There are several popular brands of digital pitch correction software other than Antares/Auto-Tune.

Do mastering engineers ever apply digital pitch correction to the vocals on finished masters? Is that even a thing?