The given statement is false.
Electrons are negatively charged and do contribute to the overall charge of the atom.
An atom is neutral in charge because in an atom the number of electrons is equal to the number of protons. So the overall negative charge of the electrons is balanced by the positive charge of the protons.
However, if the number of electrons ( negatively charged) is greater than or less than the number of protons (positively charged ), then the atom will no longer remain neutral and it will become either a negatively charged ion (anion) or a positively charged ion (cation) respectively.