Yes, that is the argument to back up trickle down economics. But that's not how it works in real life. In real life, the extra money goes to the investors, AKA the rich. They get richer.
The company continues giving its employees the standard 2% cost of living increase. The rich get rich, the middle class stagnates.
Trickle down benefits no one except those at the top.
Regarding your second paragraph (which I separated for ease of reading) when the poor spend their money, theyre spending it at local stores, groceries, contractors, workers, people that contribute to the economy. When poor people get money they spend it, contributing to the economy overall. There can be no argument about this. It's a fact