Yes. Typically, to multiply two n-bit numbers, you need n - 1 n-bit adders. You basically do long multiplication.

I'd upload an image but either voyager or my instance won't let me for some reason, so sorry if this doesn't embed right

Conceptually yes, but you can achieve better efficiency by putting multiple adders together with e.g. a Wallace tree.

There are more efficient ways to expand adders than simply chaining them as well.