So no, this will not increase inflation. The goods produced matches the money spent, so demand and supply continue to match up.
Inflation would occur if production ceases, but demand continues to remain the same (or higher).
Whatever the way you see it, that 100 million of buying power should not exist and eventually ends up lifting the prices of normal goods just with the economic activity it generates.
But the thing is, there hasn't been that much money printed by the FEDs or the US gov't. The stimulus cheques are not money printing, but money borrowing - a major difference. Borrowed money needs to be paid back, and so there may be temporary inflation caused by said stimulus, but it's clawed back in the future when the stimulus' effect has worked!
Imagine this: you need $100k so you come to me, and I write you a check. BUT: you're not allowed to cash that check. Instead you use it as collateral for a $100k bank loan. But the bank is not allowed to cash my check either, it can only put it into safety deposit box. And if you default on your loan bank will put that check on auction. So, time flies an no one ever tries to cash my check. And if they ever tried they would find that I never had that $100k in my account in the first place. I "printed" that money when I wrote the check. That's how "borrowing" between FED and Government works, and that's why it is money printing. FED is bluffing about having all that money, but no one is legally allowed to call their bluff.
Also: no, those loans will never be repaid. With Modern Monetary Theory debt can only increase in nominal value, until US follows the trajectory of Venezuela, becoming a failed state with hyperinflation.
The US government owes money to the US government. The trend is an uptrend.
The only thing stopping this stratagem is currency devaluation on the free global market.