If you have dilated cardiomyopathy caused by prolonged arrhythmia, would it go away when treated properly? Or is damaged- damaged and won't go away?

Yes. frequent cardiac irregularity such as ventricular premature beats including those considered benign like outflow track PVCs can cause a cardiomyopathy which can be reversible by catheter ablation. This is a possibility when an underlying structural heart disease is ruled out. A cardiologist can help sort this out.
Gets better. I agree with Dr. Yap-arrhythmia related cardiomyopathy is reversible by suppressing the arrhythmia, either with drugs or by catheter ablation. Usually a combination of drugs (angiotensin inhibitor and betablocker) is also used to enhance recovery.
See a cardiologist. Arrhythmia is a symptom of cardiomyopathy, not the cause. The course is highly variable, i.e. different in almost every patient. Presumably you are under the care of a cardiologist, right? If so, ask him or her and follow the advice you get. If not, see a cardiologist ASAP and take it from there. Good luck!