Yes this is a cause of inflation, but not the cause of inflation today.

Today, much of the inflation is cost-push instead of demand-pull like you described. Cars became expensive, not because suddenly everyone had money to go buy a car, or suddenly those peaky autoworkers caught a raise, but because the parts to make the cars didn’t exist because of supply chain problems brought on because of Covid lockdowns.

Eggs are expensive because chickens are dying of avian flu, not because undocumented laborers getting an extra nickel.

Same with oil, grain, pretty much everything.