There is a limited pool of money. If it weren't limited, it wouldn't be worth anything, as scarcity is the main factor in determining value.
In one sense this approaches being right, but broadly it's completely wrong.
The sense that this is right is the sense in which the various national banks/reserves try to keep this fairly true. The world works on fiat currency so limitations on the pool of money are entirely arbitrary and determined by the governments that control the monetary supply. But in reality the actual size of the pool is less what is managed and more the end 'value' of money, through controlling inflation rates.
The biggest problem here is that inactive money is entirely valueless. Money only matters when it is moving from A to B. The actual pool size doesn't matter much compared to the transactions taking place. The movement of money determine the value of money far more than the actual amount in the economy. An economy suffering from too little money moving around can take an increase in total money in the pool (say, a government stimulus) with minimal to negative impact on inflation given the right circumstances.
The total pool of currency that exists is basically representative of the total sum of actual non-monetary stuff in the world.
Again, it's only the transactions that matter. If I hoard a billion dollars I would theoretically control a negligible fraction of the world's worth, given any measure going by production. However, spending that billion dollars in concentrated ways I could have a far greater impact, as a billion dollars is always a significant transaction and powerful market force. The impact of concentrated currency exceeds it's stationary value by far.
This is true even on the lower scale, but in different ways. Having a hundred dollars in the bank gives you few economic options. Having a thousand gives you far more than the ten-time buying power would inherently suggest. That tenfold increase is more like a hundred-fold increase in economic power. Going up to ten thousand is an even bigger increase in power. A hundred thousand and you can start exerting serious economic influence, far, far beyond what you can simply buy with the money from the perspective of the guy with a hundred bucks and change.
But going back to the point, stationary money is money not exerting economic influence. Not representing 'stuff'. So if people were truly just removing money from the system by hoarding it they would have minimal-to-no impact on the actual market. They could always distort markets by joining them later, but while just sitting on mattresses made of money they aren't actually doing any real damage.
In reality such savings do impact the market through their investment and management, but that tends to be through the abstraction levels of investment vehicles and funds.