Nope.
The fielded quite large contingents of subject people, mostly Lybians and Libo-Poenicians, as well as allied people - Numidians, Siculi etc. People of Libya had to give qute substantial numbers of men-at-arms into Punic army.
Besides the Carthaginian citizens manned warships, which also meant quite a large war effort, given the numbers of ships - and there were always far less carthaginian citizens than Roman citizens.