I think some might out of curiosity on their side.
I know some girls that work in admin that seem to stalk some candidates on their off time.
So yes the possibility is there.
But unless as stated above, you post sexist/racist etc content on your socials, I think you have nothing to worry about realistically speaking...
Which is why you probably want to make your privacy settings private on all socials, unless you dont mind making it public and have nothing serious to hide...
As stated, normally you dont have time neither would you be concerned in doing a full background social check on students, its just not realistic.