Actually, yes, we have the absorption/transmission spectrum of pure water very well measured. the blue end of the spectrum passes with minor absorption whereas light absorption increases to a peak in the unfrared. We can do those measurements with such precision that the difference between deuterium water (heavy water, D2O) and regular H2O is clear. the difference in mass shifts the absorption region due to the mass effect on vibrational energies.
Hydrogen in H2 gas does not behave the same as hydrogen bonded to another element, in another compound, so it really does not matter what the spectrum of hydrogen is, for this particular question.