They generally address those issues separately. It won't look good for him if the court sees a bunch of pictures of him traveling around the world drunk off his ass while claiming poverty.
I think they'll say he can afford to take a few less holidays and pay some more. And if it keeps adding up, it eventually hits felony non-support level and he'll either have to live as a fugitive or get extradited. And actually in California, it's a mere $2,500 in missed payments, although they usually wait until it gets a lot bigger because it's not worth the effort of forcing the deadbeat felon to pay up $2,500, then have to do the same again in a couple months.
They wait until it gets up often into the six figures and then put you behind bars where you get to figure out how to get that money together or else just rot there.