Can a California court grant an order for spousal support if the divorce was obtained in Texas?

You should get advise from a California attorney.  Ask the attorney if there is a cause of action for alimony or spousal maintenance that is independent of any divorce action.  That is the operative question because a California judge has no power to deny, alter, change, or amend a Texas divorce decree and in Texas alimony is unconstitutional (we have a limited statute for spousal maintenance which is another topic).

In other words, if you divorce in Texas and then move to California "after the Texas Divorce is final" a California judge cannot screw with the divorce or any terms in the divorce including awarding property differently or giving her spousal maintenance as part of the divorce.  The U.S. Constitution contains a "full faith and credit" clause that ensures marriage, divorce, adoption, and other matters ruled upon by courts in other states remain affective in the new state.  This is why you do not have to remarry when you cross state lines.