Yes, but the state will take more than it gives from the billionaire. This is actually more bureaucratically efficient than manually means testing every possible recipient.
How would they take more from the billionaire? Means test them? What if they're asset rich, cash poor... or if they have no income?
The whole idea is unworkable. It's like it's been dreamed up by a 5 year old.
In the current system, yes. But at least we do away with one set of means testing. I would actually argue for a flat tax rate in the presence of a basic income. As for "asset rich, cash poor, no income" there are plenty of ideas out there for capital or capital gains taxes.
The point of it is that our technology is far outpacing our own capabilities, and pretty soon you'll have to literally become a robot in order to compete for basic income. Instead of allowing only the 1 percent of the rich people to own everybody else, we'll have them pay for everyone to live comfortably so they can do good works, while the rich continue to have their robots do all the work. Everybody wins.