Not as such. Sure such things are irrecoverably linked but by itself OOP is not "just classes and all that". I have further troubles as things like LISP work in such a way that you can reinvent OOP in a language that technically lacks it, or lacked it originally.
I am also not the greatest student of computer language theory, it is how I have learned to program but that means little here.
As you say though OOP is basically standard right now with plain C being about the only language in common use that lacks it. The legacy of C means much though.
I am not sure how it is taught either, if it is like I sometimes see HTML being taught where CSS is divorced from it then we might be in for problems. I try to keep up with intros to programming type things but there are only so many times I can be introduced to typing and the concept of variables, often as explained to someone the author seems to view as a moron for not knowing programming. As mentioned above though it is not that radical a concept and you might have learned it even if you did not know you were learning it.
Beyond that various languages have subtly different ways of doing things which might cloud or render something broad I say to be wrong. If I can generalise though it represents a fundamentally different viewpoint from procedural/function programming, which is what things before tended to do. It does this by allowing access to and manipulation of data at a much finer grain level than is easy with procedural, often in a far more extensive (and extensible) way too. This has ramifications all over the shop, some good, some bad, some bad if the programmer is bad, some technically bad but able to be ignored if you have a machine with some grunt and all quite far reaching.
I think I will leave it at
Call it "just classes and all that" and you will not be too far out of line, however if you do have to drop down to C or something you will miss it so much.