Yes. Having extra cash means you can eat out (saves 1+ hour a day), buy an automated vacuum, dishwasher (extra 30 minutes a day), get a car or use taxi (1-2 hours, depending on location), hire a personal assistant (better organization, hard to estimate), get better medical care (less pain = better concentration)...
You also have access to specialists. You can hire a lawyer, people to help you with research, people to help you present yourself on social media.
In the end, you can extend your day and improve your productivity significantly, resulting in more hours available "to get lucky" effectively. I mean, being lucky when washing dishes does not help a lot, but being lucky when shopping for business opportunities...
Additionally being rich gives you a network of friends who are also rich, resulting in even more opportunities.
Your friend who owns a house in Chamonix and will let you use it for free during your vacations, your friends CEO of a big company who will give a high level internship to your son, your friends starting a new company and asking you early if you want to invest in it, etc...
Being rich is like getting extra at-bats in a baseball game. If you're normal or poor, you typically get one strike and you're out. You saved your capital, invested it, and if you fail, you're gone.
When you're rich, you get to swing several times at the ball. When you miss, you fall back to your wealth/family to support you while you save up for your next swing. Then, when you finally hit, as you're running the bases you can boast to everyone about how self-made your success is.
When you're filthy rich, you have infinite at-bats, and basically it doesn't matter how good a baseball player you are, you're going to win.
Oh yes, but depending on where you live, these effects kick in way under the "being rich" threshold. (America with its strange and expensive healthcare being an outlier in the developed world, I understand that.)
What I was speaking about was the simplistic "more of X, more of Y" approach of the OP, though I understand that it was mostly sarcastic in nature.
I would even argue that there is a sweet spot where you have enough money to live comfortably, but not enough to be a promising scam/crime target.
You also have access to specialists. You can hire a lawyer, people to help you with research, people to help you present yourself on social media.
In the end, you can extend your day and improve your productivity significantly, resulting in more hours available "to get lucky" effectively. I mean, being lucky when washing dishes does not help a lot, but being lucky when shopping for business opportunities...