Your statement is headed in the right direction, but misses some important subtleties. Money in the bank, even if you never spend it, can have velocity because the bank can use that deposit money for fractional reserve lending. Also, and very importantly, velocity has a multiplier effect, so small changes can be more important than one might intuitively expect. If you dramatically increase money supply, but velocity dramatically decreases, depending on the relative amounts of both, you may have inflation or deflation. In other words, both aspects supply and velocity are important.
This ties into the infamous parable of the Greek hotelier, where you can see that it is the movement of money that has the greatest impact on the economy:
It is a slow day in a little Greek village. The rain is beating down and the streets are deserted. Times are tough, everybody is in debt, and everybody lives on credit. On this particular day a rich German tourist is driving through the village, stops at the local hotel and lays a €100 note on the desk, telling the hotel owner he wants to inspect the rooms upstairs in order to pick one to spend the night. The owner gives him some keys and, as soon as the visitor has walked upstairs, the hotelier grabs the €100 note and runs next door to pay his debt to the butcher. The butcher takes the €100 note and runs down the street to repay his debt to the pig farmer. The pig farmer takes the €100 note and heads off to pay his bill at the supplier of feed and fuel. The guy at the Farmers' Co-op takes the €100 note and runs to pay his drinks bill at the taverna. The publican slips the money along to the local prostitute drinking at the bar, who has also been facing hard times and has had to offer him "services" on credit. The hooker then rushes to the hotel and pays off her room bill to the hotel owner with the €100 note. The hotel proprietor then places the €100 note back on the counter so the rich traveler will not suspect anything. At that moment the traveler comes down the stairs, picks up the €100 note, states that the rooms are not satisfactory, pockets the money, and leaves town.
No one produced anything. No one earned anything. However, the whole village is now out of debt and looking to the future with a lot more optimism.