Hi Cesare,
Adwords top three ads appears above organic results, even if you are on top in organic for the queries,user may get attracted with adwords ads as they have proper call to action, sometimes prices sometimes offers and also sitelinks, call extensions etc.
So IMO you shouldn't turn off adwords campaign even if you are ranking on top position in SERP.
More times your domain will appear more it can catch users eyeballs.if user see ad from single domain more then once they are more interested to click on your ad.
Run a campaign for a week, turn it off for another week, then on again and off again and see if you can detect any pattern.
Thanks