Well, of course it is important. It's usually referred to as a "chemical shift" like in NMR and it is highly dependent on the state of the atoms.
A primitive example: if you have single and double charged cations of the same species in your solid, the double charged ion of course has less electron density which results in a stronger interaction between the nucleus and the remaining electrons. Therefore these will have a higher binding energy which results a lower kinetic energy in comparison with the single charged ion. [For anions, it's the other way around, of course.]
Thus, you can deconvolute the signal of a specific element and learn something about the distribution of chemical states. A "textbook quality" example of this can be found in this work:
Article Atomic Oxygen on Graphite: Chemical Characterization and The...
One more thing: you're observing electrons, not photons. Therefore I would not recommend to use the terms "blue shift" or "red shift".