Can an ukulele have a metal string without breaking it?

Maybe, depending on the Ukulele. The uke is designed to be strung with gut or nylon strings. Metal is very likely to over stress the instrument. The larger ukuleles are more likely to have a metal string.

Note that some strings, such as those for a banjolele or a bass ukulele, are wound with very thin wire to make it vibrate in the correct areas.