having wider tyres will improve grip in some extent ...
maybe - depends on your definition of 'improve' - however, it certainly won't 'increase'
with wider tyres, you'll get marginally better lateral grip, and for the front tyres at least, the slip angle will be improved. However, you'll find that slides become less progressive and you'll risk snap-oversteer if you fit wider tyres to only the front.
FWIW, I run 215 section tyres, despite my power figures. I have very little problem with traction in the dry, and rarely in the wet either