Simple answer is no, the FAA is a safety regulator, only CASA is a Commercial Activies Regulator.
Not quite that straightforward. In FAA-land these things are indirectly regulated via the privileges of the license you hold (and the maintenance regulations covering the a/c itself).
In the OPs scenario, if he holds a PPL only, then the operation he proposes would definitely be illegal, as someone is paying for the a/c hire. If CPL, then fine (
AFAIK at least).