In OFDM, does $N N^H$ equal $I$?
You're conflating two different definitions of orthogonal.


Orthogonal in the OFDM sense means that the subcarriers are mutually orthogonal to one another from the perspective of a correlator-based receiver (the optimum receiver for the AWGN channel).
An orthogonal matrix $\mathbf{A}$ is one whose columns are all unit vectors that are jointly orthogonal to one another, such that $\mathbf{AA^H} = I$.


These two concepts aren't related; there is no constraint on the modulation applied to the various subcarriers in an OFDM symbol. The orthogonality is imposed via careful choice of the symbol period and subcarrier spacing, typically implemented using DFTs since it conveniently provides the desired time/frequency grid.