Can the idea of entropy be extended to orbitals?
No.

The reason why a gas particle in a large volume has a large entropy is not because it has a lot of space to move around per se. A better explanation is that for a given energy, there are many accessible translational states (these states can be derived from the particle in a box model). If we assume that all of these translational states are equally likely to be populated, then the number of possible microstates for the system, $W$, is large and hence $S = k \ln W$ is large.

An electron in an orbital isn't whizzing about, and an orbital most certainly isn't a container of variable size for the electron to move around in. An orbital is simply one (electronic) state of an electron.

Therefore, it doesn't make sense to talk about the translational states of an electron that is moving about in an orbital. It also doesn't make sense to talk about the translational entropy of an electron as being larger in a larger orbital.