  Using optical magneto-spectroscopy, we investigate the magnetic excitations
of Na$_2$Co$_2$TeO$_6$ in a broad magnetic field range ($0\ \rm{T}\leq B\leq
17.5\ \rm{T}$) at low temperature. Our measurements reveal rich spectra of
in-plane magnetic excitations with a surprisingly large number of modes, even
in the high-field spin-polarized state. Theoretical calculations find that the
Na-occupation disorder in \NCTO plays a crucial role in generating these modes.
Our work demonstrates the necessity to consider disorder in the spin
environment in the search for Kitaev quantum spin liquid states in practicable
materials.
