Yep. Grade school multiplication of two large numbers is the same thing (except for the carries) as convolution of two signals in the time domain. The numbers are the signals. You already know that piecewise multiplication in the frequency domain is equivalent to (and faster than) convolution of those signals in the time domain. So that's what FFT multiplication is about.

It's only useful for VERY large numbers (thousands of digits), which is why most people never encounter it.