Answer
No, the 2 spectra will have different lines. We expect to see only Lyman lines in an absorption spectrum of room temperature hydrogen. But Lyman, Balmer, Paschen, and other emission lines will be present in the spectrum of high-temperature hydrogen.
Work Step by Step
Consider an absorption spectrum taken at room temperature. Nearly all the atoms are in the ground state, n=1. The absorption spectrum will contain only the Lyman lines, because the photons absorbed are those that start at n = 1, and transition to higher levels.
Now consider an emission spectrum of hydrogen, taken at very high temperatures, when some/many atoms are in excited states. The electrons starting at high n values fall to many lower energy levels, for example, n = 2 or n = 3, not just down to the n = 1 level. So, the emission spectrum will contain the Balmer series, the Paschen series, etc., not just the Lyman series.
