In my limited understanding, yes, it's possible. But it would require significant international effort to get the super rich, the ones that can pay fabulous amounts of money to money launderers legal tax experts that know just the right loophole to ensure that mr. billionaire will pay only 500k in taxes rather than 10 million, because tax havens only exist thanks to certain countries' very lax rules on banking.
There are already large numbers of treaties in place for countries to cooperate in tracking down tax evasion. It might not be as expensive as you think. If you think of it from a practical standpoint, we have lists of the richest people in the world. That's an excellent starting point, isn't it?
If some billionaire is claiming that they actually aren't a billionaire, and that the lists are wrong, when some government is trying to tax them at an exorbitant rate, it's likely that they will give all of their banking details to said government to prove it. Or they will hide those banking details, and they'll be forced to pay the taxes.