They are eligible if he is.
The founders excluded foreigners, including the children of foreigners, who are born with the foreign nationality of their foreign parent(s), from being President with the natural born citizen clause for very good reasons.
Ted Cruz’s fealty to the Constitution ends where his ambition starts.
Any number of individuals could be conferred eligible but your choice of violent anti Americans like alwaki is heinous.
The 1790 Congressional statute speaks precisely to his birth situation and finds him natural born. The Constitution does not say “born in the United States”— something that could easily be conveyed in the text. The 1790 law is clear.
Cruz can be President of United States.