Can short messages backed up by backup software be used as evidence?

Yes, but if it is not notarized, the probative force of the evidence will be low, because it is electronic evidence, and it is also copied electronic evidence, not original evidence. I suggest you look for other evidence, such as the record of sending and receiving SMS provided by the operator, and compare it with the record provided by you. But in short, such evidence can not be used as the main evidence, but generally can only be used as supplementary evidence.