Can we apply Nodal Analysis to non planar circuits?
Yes, nodal analysis works for non-planar circuit. You treat non-planar circuits exactly the same way you treat planar circuits (which is why I was unfamiliar with the term: this restriction seems to apply primarily to mesh analysis, which I've never really used).

Asside:

The primary special case with nodal analysis is handling voltage sources. There are two ways this is handled: using supernodes, or using modified nodal analysis (MNA). Both mathematically do roughly the same thing, but MNA is a formalization of the process to be extremely systematic such that even a computer can take a network in and solve it (MNA is the basis for SPICE).

Circuits where nodal analysis or its derivatives don't work are those with no mathematically well defined answer (i.e. the equations produce contradictory statements):







simulate this circuit &ndash; Schematic created using CircuitLab

There are ways to get around these mathematical contradictions by introducing reality to the model (voltage sources have some non-zero series resistance, current sources have some finite parallel resistance, etc.), but that's already well out of the scope of this question.