Can a penguin survive in a desert?

Your premise is incorrect. Penguins do live in deserts. Almost the entire continent of Antarctica is desert and penguins live there. Along the coast of the Namib Desert in Africa you will find the African Penguin and on the Pacific Coast of Chile you will find the Humboltd Penguin who nest in the cliffs there. The penguins seem well suited to their desert habitats.