It is unlikely, because they are carbon. We are made of carbon, and the body typically doesn't recognize it as a threat.

This is the main reason that coal dust / black lung is so bad. Our lungs have all sorts of things to clear the detritus, but carbon isn't recognized as something that needs to be cleared :(

The vaccine itself (nanolipid with smrna center) likely is though, as well as the spike poison it induces.