No, in reality, electrons in atoms with Z>1 (more than one proton in the nucleus) do not occupy one-electron spin-orbitals. The concept of one-electron spin-orbitals is a simplification commonly used in introductory quantum mechanics courses to help understand the behavior of electrons in atoms.
In reality, the behavior of electrons in atoms is described by a more complex model called the multi-electron wave function. The wave function represents the state of the entire electron system in an atom, taking into account the interactions among all the electrons. The presence of multiple electrons leads to electron-electron repulsion, which affects the distribution and behavior of the electrons.
The multi-electron wave function includes the effects of electron-electron interactions and the phenomenon known as electron correlation. Electron correlation refers to the fact that the behavior of one electron is influenced by the presence and behavior of the other electrons in the system. Electron correlation plays a crucial role in determining the properties of atoms and molecules.
Therefore, while the concept of one-electron spin-orbitals can provide a useful framework for understanding the behavior of individual electrons in atoms, it is an oversimplification of the true behavior of electrons in multi-electron atoms.