No. First, inflation is having too much of a currency, not too much wealth. In fact, inflation normally means that the amount of currency exceeds the growth of the economy. If your theory is that the billionaires' money is just lying around and being re-injected into the economy. Since only the government can create money, this money already exists in the economy.
Physical cash is valuable for one of three reasons: fiat (the government says it's worth something), currency-peg (the government says it's cash is worth so much of someone else's currency), or a commodity-standard (the government says it's worth so much of a thing that people will trade for, e.g. gold, silver, jewels, oil, rice). A commodity-standard is largely dead in the global economy, with most nations using fiat (the U.S. dollar is valuable because the government says it is, and the U.S. economy trades in it exclusively, and everyone wants a piece of the action) or will peg to a currency (the government will give you 2 PegBucks for every $1 you give them) and will then try to keep their ratio equal (if the purchasing power of a $1 this week falls to $0.99 next week, then 2 PegBucks will still buy the same amount of goods as $1... it's just a smaller amount of goods, so the price in Pegbucks and Dollars rises and falls at the same rate).
Now, all that said, most billionaires are not billionaires because they get money from other people and put it into a huge pile of coins and bills in a giant vault complete with diving board so they can swim in it. (Look, when you find out that the remake of Ducktales cast David Tennant as Scrooge McDuck, and the first episode is literally titled "Woo-hoo!", you sit down, shut up, and watch the duck swim. And actually, the Scrooge comics that Ducktales is based on do show a lot of problems with "simple solutions" of economies so... they do discuss how the famous Money Bin is a luxury... Scrooge can afford to swim in all that gold because he's got more money that's not sitting in his vault.)
In reality, most people are billionaires in "Net Worth" which means they don't have bank accounts with all their money stored in the bank... Stocks are only valuable because the company is valuable and a share (one stock) gets a cut of that profit. Even if you put it into a bank, it's not removed from the economy. Banks also give loans, remember. They aren't creating money, but using the money given to them by their account holders to invest in other ventures and charge loan holders interest on the money for as long as the loan is not returned (the idea is that the person can, within a set time, earn the money they are requesting, but they need the money now and will pay back a small portion of that money over time, plus a little extra... if you are putting money in the bank, you receive a cut of that returned interest because it's your money, not the bank's.).
Either way, a billionaire might be worth something close to 10 or 11 digits of value on paper, but that's not all cash on in the bank (aka liquid assets), and in fact much of it is tied up in other ventures. Let's say I have an assembly line that makes something, and one machine on the line costs $100,000, and I have five of these machines in my factory. My stock is a symbolic representation of everything my company is worth so if I have 51% controlling interest, then for every $100,000 machine, I own $51,000 of it. Multiply by 5 for my factory (($255,000 for all machines) and add that to the price to build my factory building, the price to own the land my factory on, the price of any other offices, all my personally owned stuff (fancy house, fancy car, cool toys) and my bank account values and that's my Net Worth, which can be millions or billions of dollars all totaled out. And some of that cannot be 100% recaptured (I'm not fixing my machines... I got a guy I can pay to do that for me... that's money that isn't coming back to me... but if I don't pay it then I can't make things and I sell those things to afford all this stuff.).