Several people have answered this with essentially: “No, because terraforming is unfeasible and expensive”. I’ll try and answer this question under the assumption that terraforming and leaving is feasible to do.
The core argument against billionaires is that they hoard wealth that they didn’t produce.
Instead, it’s the billions of humans that turn work into value, whether that’s by turning a log into planks, planks into chairs, or by managing the sales operations that allow the sale of those chairs to others.
The 3.5k-ish billionaires in the world didn’t create a billion euros worth of value themselves, they captured most of it from other people’s work, under the justification that they provided the startup capital that allowed the plank maker to buy the log, the chair maker to buy the plank, and the sales managers to buy the chairs to sell. Depending on your ideology this is either justified or not (labour theory of value)
Because of this, getting rid of all the people that generate this wealth inevitably destroys the wealth itself, meaning that: no, they couldn’t just abandon earth because we are the ones that actually create the wealth that allows them their lifestyle. No one to cook, no one to clean, no one to build giant yachts means no billionaire lifestyle.
Now, the newest question at hand in a lot of economies is: will AI and robotics essentially allow billionaires to actually produce this wealth without other people?
Even though research suggests that lots of jobs could be lost, “lots” doesn’t mean all. However, I assume in part your question is motivated by the thought that billionaires will destroy the planet in an attempt to answer that question.
If they CAN, then this means someone still needs to build those robots. That’s probably not going to be the billionaires themselves, so it’ll be us the people doing that. In that case, the only thing stopping us from just making more, until none of us need to work anymore, is the billionaires telling us so.
If they CAN’T, they also can’t leave us behind without also leaving behind pretty much all of their wealth and us just continuing on our way without them, presumably with less being skimmed off the top.
The last caveat to this is, of course, the ruined planet. This is a tricky one, but comes down to a numbers game. We outnumber billionaires by a lot and can drive the change we want by voting and pushing for regulation that benefits the many, not the few.
So, tl;dr: If they want to leave, they need to bring us along, and then they may as well not move, so we pretty much need earth.
While I’d argue in practice there is a pretty significant difference in capability between household labour, advance materials refinery, and workforce management for the sake of this argument we are obviously assuming hyper advanced robotics and in that case you’re 100% right.
However, going back to my argument of “if they can replace all labour with robotics”: in that kind of situation, what’s to stop us from making more until every job is covered by robotics?
Then none of us need to work, and the entire concept of a billionaire becomes irrelevant.
And who even cares if a couple thousand people decide to leave with some robots? They still won’t be able to bring the majority of their wealth and in that case all the more for us left on earth.