Uh, no.
Trump’s mother was naturalized on March 10, 1942, over four years before Trump was born.
She took an oath to renounce all other countries’ claims upon her.
His father, Fred Trump was born in America. So, Trump is born of two American citizens.
By your logic, since Canada is a dominion of Great Britain, then Cruz still has a claim of Britain on him.
Do you really believe that?