Could fluoride rinse really prevent tartar buildup?

Not really. Fluoride rinses are helpful with preventing tooth decay but only mildly helpful with plaque removal and hardly at all with preventing calculus buildup. There are some rinse additives that claim to prevent calculus buildup but studies don't bear it out. The best way to reduce calculus and tartar build up is with physical plaque removal with a toothbrush and floss and regular dental cleanings.