I don't think so. Not all teaching is historically pink collared work, so teaching as a category wouldn't necessarily fall under that category. Even the Wikipedia page being cited agrees that teaching depends on the level (and I'd also say subject).

Not all teaching would be considered pink-collar work, though, and other definitions don't rely on work necessarily being pink-collar. If you have Wikipedia open, you can keep reading the Working Class page. Here's another definition given that would exclude teaching

It lines up perfectly well with the standard socialist use of the term. Which, to be fair, is certainly overrepresented here than would be in the US at large, but it's weird for that definition not to be acknowledged here.

Presumably it would be along the lines of blue collar workers or less than middle class. This is also probably the most common definition held in the US, since the vast majority of people don't know anything about socialist theory.