This is wrong.
1) Hydrogen gas molecules, at pressure, don't have a spectrum that looks like the atomic spectrum at near-vacuum that the Paschen series is about.
2) Almost no hydrogen gas is in an excited n=3 state at room temperature (or anywhere near it), for which reason you wouldn't see much absorption in those lines anyway.
3) It does not require precise measurement to see Paschen lines. Do you know what a typical resolution of a spectrometer is? Less than 1 cm-1. The first Paschen lines are separated by thousands of cm-1.
4) IR spectroscopy, as a rule, looks at vibrational and rotational transitions, not electronic ones.
5) IR/Vis/UV spectroscopy does NOT require that a molecule be 'broken up' into atoms at all - (or you wouldn't even have vibrational/rotational spectra).
6) Spectroscopy in general doesn't require any such thing either. You think molecules don't emit and absorb radiation as well?
The only major issue measuring the IR vibrational spectrum of hydrogen is that it's homonuclear, which means you have to use Raman.