If you want to go a little overboard it's possible to use the C abi and write a thin wrapper in C++.
Unfortunately not. Node is bound tightly to V8, which is very C++.
You can, though, use things like node-ffi.
Doesn't that make the answer "mostly yes, but you need to write the binding in C++"? I.e. write all your code in C, then just call the C methods from the one C++ class you must write.
You can write the library/addon in C and then define the bindings with JavaScript using various npm libraries. There's no need for C++.
Eh, by that logic, we can write Node extensions in Fortran or Brainfuck.
I think it might be possible to do it with some sort of wrapping library written in C++ with C APIs. Technically, it will work this way for every kind of C++ library.