Yes, there would still be inflation, as long as the new money was actually spent and not locked away in a vault somewhere.
What would happen if the Treasury Secretary got drunk one night and secretly hacked his personal bank account to give himself a trillion dollars of new fiat money?
If he never spent it and no one ever knew, nothing. Money would only change prices if it got spent.
But suppose the Secretary retires the next day, and goes on a massive spending spree buying all sorts of luxury goods and stuff, and everyone is too dumb to realize that something is fishy.
Well, what results? It means that people who sell gold-plated toilet seats and caviar and yachts and mansions notice that they’re selling a lot more gold toilets than they used to. Sales are up! Sell more! Raise prices! More money in our pockets! The price of gold toilets rises as stock gets sold. As they make more they need more gold and porcelain, so they call the gold dealer and porcelain dealer and order more, gold just got more scarce so the gold dealer raises prices.
The toilet maker and gold dealer are making more money, so they deposit it in the bank. The bank has more money so it starts lending more money. More people get loans, suddenly it’s easy to get money. Plenty of people now have extra money in their pockets, so they go to spend it, but since everyone is buying more stuff than they used to businesses are raising prices, and selling everything even at the new higher prices since people still want the stuff and now have extra money.
Businesses have to pay more for their goods, and so the people who make goods are selling more, which means they increase production and hire more workers, which means people are getting higher salaries, only it doesn’t seem to help because somehow everything is more expensive than it used to be.
So what has happened is that the new trillion dollars goes out into the economy, is used to bid for goods and services, and merely increases the price that can be charged for goods and services. The classic definition of inflation is “too much money chasing too few goods”. Prices rise in the aggregate because when prices are raised people are still willing to pay the higher prices, and they’re willing to pay the higher prices because they have more money than they used to. Or maybe they don’t have more money, but someone does, and those people keep buying stuff at the higher prices, so people who didn’t get a raise have to pay higher prices even though they have the same income as before.
But note that injecting money into the system can result in more production as people try to grab that money. This is what the government tried to do during the recession, add money to the economy to stimulate it.