No it doesn't. A website's own preferences fall under the 'necessary for site functionality" exception.
Besides how many sites actually have this as the only reason for cookies? Every time I get a new cookie banner I check it and there's always lots of data shared with "trusted partners". Even sites of companies that purely make money off their own products and services and shouldn't need to sell data. Businesses are just addicted to it.
The only provision I like is that they may only ask once every 6 months. However personally I wish that they'd make it a requirement to honour the do not track flag and never ask anything in that case. The common argument that browsers turn it on by default doesn't matter in the EU because tracking should be opt-in here anyway so this is expected behaviour. The browsers would quickly bring the flag back if it actually serves a purpose.
I'll keep blocking all ads and tracking anyway.