Like, I could see some people noticing that the book they're reading has dashes that are a bit longer than normal, but what made you think "That must be it's own thing, separate from a normal dash" as opposed to something like "In this font the dashes are very long"?
Also, it's called em dash because it's as long as the letter m (as a rule of thumb), so it's usually an easy visual comparison. Finally, a typeface with hyphens as long as em dashes would be terrible and quite noticeably wrong!
The em-dash is indicative of AI usage when it shows up in contexts where it doesn't belong. Like informal context like forum comments and emails (though "smart" substitutions do complicate the picture a bit).
I'd only be funny if they argued it indicated AI usage in context where it does belong, like formal writing.
I think you have to make a distinction: there's using a dash as you describe and using the actual em-dash character. Without an smartquotes-type autocorrect-type feature (which admittedly is common in certain apps/platforms like Outlook and Word), an actual em-dash is awkward to type. I'd expect someone using it informally to just use a regular dash (-) or two (--).
I think you're automatically in a pretty formal writing context if you care if you use an em-dash character or not.
Which brings up an interesting idea: would Microsoft turn off it's smartquotes-type autocorrect, because now it makes you look like a dumb AI-user? Probably, if they cared about their users. But I doubt they will because they're so into hyping AI that "Microslop" is a thing.
I have known people that personally used em-dashes in all the wrong places way before AI... entire emails would just be paragraphs-long run-on sentences filled with dashes.