If I have an hydrogen atom at $T=0K$ from Boltzmann distribution I can have only the G.S populated, so if I send to this atom photons at all energies is impossible to excite the atom, is this right? If this is right, the energy spectrum of this atom would be flat?
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If I have a single hydrogen atom with an electron in the ground state, can light of the correct energy excite this electron? The answer to this question is yes.
To bring in your discussion of equilibrium statistical mechanics phenomena, it is best to consider an ensemble of hydrogen atoms at zero temperature. Then your question may be recast as: can light excite electrons in the hydrogen atoms of this ensemble, which will lead to an energy distribution that is different to that predicted by the equilibrium statistical distribution? The answer again is yes. Your are driving the system out-of-equilibrium by using light to excite electrons, so your equilibrium distribution no longer applies.
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