In the stern-gerlach experiment, silver atoms with a +1/2 would be deflected up, and atoms with a -1/2 spin would be deflected down. With that in mind, would electrons' orbitals within an atom be affected by its spin?
It's more accurate to say those numbers as the electron spin projection in a given direction, or the eigenvalues of operator ##S_z##.An electron's spin can either be either +1/2 or -1/2, that's what the stern-gerlach experiment tested.
it really depends on the system, if the Ag atom is isolated its orbital won't be effected by the sign of the z component of the spin. However, as pointed out in comment #2, if there is external magnetic field, the energy levels are no longer degenerate in ##m_j##'s, rather it will split into different energy levels.And if so, wouldn't the electron orbitals differ depending on the sign of the spin?