Unconnected is the worse scenario, as to noise reduction be more specific... EMC noise, noise causing signal integrity problems. Adding copper pours may help then again it may not, this will not be a contiguous ground plane just some copper pours.... What ever you do on a two layer design is going to have compromises
Start by looking at Henry Otts site...
Your other problems are copper weight of the base laminate and current capacity, plus size of features to be etched, 0.035 plated up to approx. 0.052 requires a 15mm thick track for the 15A current.....