To my ear it would sound slangish, but the adjective was used in Polish. I recall it in old movies and literature, especially located in traditional urban societies. I'm not sure if it's still used in this meaning. "Klasa garniak, skąd masz?".
EDIT: on the other hand, a similar exclamation, as in the OP post would besomewhat colloquial, but still would be ok. "Dobrze wyglądasz. Klasa!" (albo "z klasą"). So the remark above treats about a specific usage of the word rather than the word itself.
The noun "klasa" is still used though, both in terms of school class, broad category of social strata (klasa robotnicza), as well as quality category (samochód wysokiej klasy, samochód klasy A).
I'm not sure about the source language, as all the words seem to be derived from Latin classis - and we have loads of Latin loanwords in Polish, either taken directly (Latin was widely used in Poland, especially among educated classes) or through Czech or German for various cultural reasons.