Sure, I believe it's useful in that rich western countries continue their leisurely transition to cleaner energy as it becomes cheaper, combined with gas taxes and carbon trading and such. Billionaires investing more money in cleaner energy can be marginally beneficial, though there is already large and increasing amounts of capital allocated by the markets toward this end.

But the deciding factor is can we make everyone stop using the cheap fossil fuels that are basically free money lying in the ground. Oil price will follow demand. It might get cheaper if western countries cut consumption, but someone will still buy the rest with the lower price. And there is nothing in the horizon that would displace oil and coal at their minimum profitable production prices for developing countries (where most people live) in the requisite timeframe. If we leave it to markets, this is the case by overwhelming odds, Zuckerberg or no Zuckerberg.

Think what needs to happen on the world stage in order to enact a global ban (1) on oil pumping and coal mining within 20 years. That's the job. Interests of nations addicted to the oil income, interests of nations whose agriculture is entirely dependent on cheap imported oil, etc. Easy UN consensus?

And this is just the energy sector, there's more to climate change drivers. So fixing this is necessary but not sufficient. The same political measures that are needed to coordinate the energy sector will also work for the other sectors. But energy tech won't.

(1) A very high tax really, that 99% prevents use in fuel applications. Ban is a simpler word.

edit: added bit about fossil prices reacting to demand in west