People started theorising this the day he announced that "religion is important to him" which I thought was ridiculous, then he hired Obama's campaign advisers, announced tour of the country and then the recent war on fake news. If he doesn't run directly he's definitely reaching for some political clout

It would be a massive loss for him. Especially with the Democrats in the middle of a war on all fronts, which is the most pressing issue of the next 2020 candidate. I doubt Zuckerberg could navigate the internal politics to find solid support. He would not make it past the primaries. He has a bigger trust perception problem than Hillary. He should wait it out a few cycles, wait for his child to get older and craft a family man image to replace his current image.