Well if you beat the game you can look for more Pokemon in the Friend Safari in other places. No real need to grind at all unless you put a Pokemon in the day care and ride your bike around Lumiose until you reach a high enough level to beat the game easier. So if you want to level up Pokemon faster you might as well go through the story mode. If you are into IVs the definitely need to finish story mode because the IV checker is in the last town you find in the game after story mode.
Depends. I for one can't play a Pokemon game twice. Not in this day and age, that is. I even skipped ORAS because I lost interest in its single player gameplay. If you're a competitive player like myself, I vote for skipping the story. Just get to the DayCare and you should be good to go.