@jurgar,
Yes, this plugin lets you do that.
It does not happen by default, because for obvious reasons, not every site will have or use the same “non functional” cookies.
Non functional means, they are not absolutely necessary to let a site function.
If you have “non functional” cookies/scripts like Google analytics, adwords, facebook pixels, remarketing scripts, you need to add those scripts ONLY to the block feature of Cookie Notice. You need to remove the scripts from their original places, they may only reside in the blocking feature. If not they will still track and wont be blocked!