Yes. Look at the oldest correlation in epidemiological demographics-socioeconomic status and health. The famous health gradient.
Research has shown that poverty leads to poor health in adulthood for children raised in poverty even when their economic status improved. Coming from long-term poverty I can tell you micro aggressions aimed at people on welfare took a toll on my health.
As I went about my day outside of school, I was only subjected to this through disclosure of my background. I was not visibly poor as someone of a different race is daily faced with micro aggressions for being visibly black.
When I run into classism, it is mostly confined to the Internet and visits with relatives. (Unfortunately, I spend all my time on the Internet). I can only imagine the health toll of that social stress from racism having lived with a milder form of it through classism.