Unsubstantiatable. The medici intermarried with royalty and have no known living patrilineal descendants. The last of whom died 7 years before mayer amshel rothschild was born.
In the 1830's the vatican was already financially stressed enough that it needed to seek a £400,000 loan from the rothschilds. With this and future loans, the rothschilds were able to eventually leverage it into the control over the vatican they have to this day.
https://populartimelines.com/timeline/Rothschild-family