Recently, I performed a MDS with Gromacs and did not neutralized the system. MD was ran and nothing happened. I wonder what will happen in a non-neutral MDS. Can it be used for analysis?
If you used PME for electrostatics, there is a uniform neutralizing plasma that is present in the system, effectively smearing the balancing charge across the system. This is obviously unphysical, but the amount of error it introduces in the system depends on how homogenous the system is. For an examination of errors in heterogeneous systems, see http://dx.doi.org/10.1021/ct400626b
It would be useful to have more information. What do you mean by nothing happens?
As pointed out before, there is no problem running charged isolated systems, but periodic boundary conditions lead to divergent electrostatic interactions.