Will C++ throw with no arguments work inside another frame to rethrow an exception?

If I have a code like the following:

try {
  doSomething();
} catch (...) {
  noteError();
}

void noteError() {
  try {
    throw;
  } catch (std::exception &err) {
    std::cerr << "Note known error here: " << err.what();
  } catch (...) {
    std::cerr << "Note unknown error here.";
  }
  throw;
}

Will the original exceptions get thrown from both places inside the lower frame of noteError()?