I doubt it, why would they? Their funding and administration are completely independent of the State of California.
The U.C. system is state-funded and answerable to the Regents of the U. of C.
Stanford has its independent endowments and can make different kinds of decisions than they could if they were in the U.C. system.
I can’t think of a reason why Stanford would want to fold themselves into the U.C. system, and not that the U.C. has much against Stanford besides some healthy sports rivalries there isn’t much reason to think pulling Stanford into the U.C. system is a good idea.