When the electronic structure of a molecule is represented by molecular orbitals, all electrons occupy molecular orbitals.
Molecular orbitals can be approximated as linear combinations of atomic orbitals. A complete basis set for the molecular orbitals is an infinite set of atomic orbitals.
A finite set of atomic orbitals will be a less accurate approximation of the molecular orbitals.
So if you represent a low-lying molecular orbital as only a linear combination of core atomic orbitals, for example the lowest energy sigma MO of NN as only linear combination of the two 1s-1s orbitals, there will be some error associated with this approximation. And if you do not include the 1s orbitals in the representation of the the higher molecular orbitals there will be some error associated with this approximation. However, in the cases that I know of the error is small.
For example, in the following early molecular orbital SCF LCAO papers, the 1s orbital are linearly combined (mixed, hybridized) with the other atomic orbitals:
[SCF LCAO MO Study of Li2][1]SCF LCAO MO Study of Li2 J. Chem. Phys. 27, 369 (1957)
[An SCF LCAO MO Study of N2][2]An SCF LCAO MO Study of N2 J. Chem. Phys. 23, 569 (1955)
[Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I][3]Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I J. Chem. Phys. 23, 1833 (1955)
As the nitrogen paper summarizes "As was expected, the inner-outer-shell mixing is extremely small". [1]: http://scitation.aip.org/content/aip/journal/jcp/27/2/10.1063/1.1743730 [2]: http://scitation.aip.org/content/aip/journal/jcp/23/3/10.1063/1.1742031 [3]: http://scitation.aip.org/content/aip/journal/jcp/23/10/10.1063/1.1740588