I suppose technically yes, but not in normal conversation (in Britain at least). It's not like it's completely nonsensical, but to us school is primary and secondary education, higher education is university; they're distinctly different things and saying "gets kicked out of school" would be way less ambiguous.
US people like to give everything a different name. They often repurpose names from elsewhere thus bringing much confusion to online spaces. It's their thing.
I'd imagine that you graduate high school at 18 and choose to go to college for the next 4, meaning you graduate as a 22-year old. Add or subtract a year for birthdays that align oddly with the academic year.
I didn't make the initial comment and I would have thought it was pretty bloody obvious I was making a joke with my second sentence. I was trying to make the explanation less dry, but thanks for the hostility. Reminds me of fuckin' Reddit.