No, the concept of electrons existing at different places at the same time, as described by quantum mechanics, does not imply that the atom becomes heavy due to the temporary appearance of electrons.
In quantum mechanics, electrons are described by wavefunctions, which represent the probability distribution of finding an electron in a particular location. According to the principle of superposition, an electron can exist in a state where its wavefunction is spread out over multiple positions simultaneously. This phenomenon is often referred to as electron "clouds" or "orbitals."
However, it's important to note that the total number of electrons within an atom remains constant. The concept of temporary electrons appearing into existence is not accurate. The wavefunction describes the probability of finding an electron in a particular location, but it does not mean that new electrons are being created or appearing and disappearing.
The mass of an atom is primarily determined by the sum of the masses of its protons, neutrons, and electrons. The mass of an electron is much smaller than that of a proton or neutron, so any fluctuations in the electron's position due to its wavefunction do not significantly affect the overall mass of the atom.
In summary, the existence of electron wavefunctions and their spread over multiple positions does not lead to an increase in the mass of the atom. The total number of electrons remains constant, and the mass of the atom is determined by the combined masses of its constituent particles (protons, neutrons, and electrons).