Question regarding resolution

As it stands, the voltage measurement offers a theoretical 9.5 bits of resolution, the current is about the same. Does that mean that the two multiplied will offer something close to 19 bits?

yes, it is similar to 12 x 12 = 144 - the number of digits grow, same for binary digits aka bits ..
That means that you need to use a long if you want to keep it in the integer domain,