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No. "Hunger haben" and "Durst haben" are idiomatic expressions. While I've occasionally heard "ich bin durstig" ('I am thirsty') from my friend's kid, he usually says "ich habe Durst", which is the usual way of saying one is thirsty in German.
In English, it's very rare to hear someone say he has hunger or thirst, but usually one describes himself as hungry or thirsty. That's what makes it a better translation.