Take any professionally made PCB and you will find that in most cases areas between traces are filled with copper areas. In fact background fills can give benefit but also be harmful to your all design. Dangerous prototypes have written a tutorial on how to make MCB background fills look professional and add additional features to schematic.
In most cases background fills are connected to GND in order to reduce resistance and electric noise. Keep in mind that filing grounds where ever it fits can also have negative effect – for instance ground planes near signal traces may add parasitic capacitance. In this case probably better use hatched fills or avoid them at all.
Sometimes it is useful to draw custom ground planes around power traces to make them more thicker in order to carry more current.