Your intuition is correct. With 0 savings there could be not only no economic growth but no economic activity assuming depreciation exists.
According to the Harrod-Domar model the growth rate of capital per worker is equal to:
Growth Rate (g) = Savings Rate (s) / Capital-Output Ratio (k)
Clearly under this model if the savings rate was 0 the growth rate of capital per worker would be 0.
This is because it is assumed that the production function has essentially only two inputs. Labor, and capital. The generic production model that is used with the Cobbs-Douglas model is
Total Output (Y) = f(K,L) = (K^a)(L^(1-a)), where 0 < a < 1.
K = the total amount of capital in a country
L = total amount of labor in a country.
a in this equation is the emphasis that is placed on either labor or capital.
Assuming that this function generically holds if K is equal to 0 that would mean that regardless as to the level of capital total output would equal 0.
So, because the growth rate of capital per worker is 0 at a 0 savings rate this means that K is a constant and unchanging.
This is where depreciation comes in. Assuming that capital goods depreciate over time the capital stock K will over time be getting smaller. Machines break, etc. In the long run capital stock will shrink to 0 meaning there will no longer be any economic activity at all.
In essence because savings goes to investment which creates capital, without any level of investment we would eventually run out capital as it depreciates leading to an output of 0.