If the amount of mass due to strong interactions changed when four hydrogen atoms went through the chain of reactions necessary to form a helium atom, then the mass of four hydrogen atoms would be different from the mass of a helium atom. So let's see if this is the case.
Wikipedia tells us that the mass of a helium atom is 4.002602 atomic mass units. The mass of a hydrogen atom is 1.00782504 amu, so four hydrogen atoms is 4.03130016 amu, and we find that the masses are indeed different.
This is of course why nuclear fusion produces energy. When four hydrogen atoms combine to form a helium atom the mass decreases by about 0.029 amu. That mass is converted to energy and emitted as the kinetic energy of the reaction products.