No. The Sahara is the world's largest hot desert (~9.2 million km²), but the largest desert overall is Antarctica.
Desert Definition: An area receiving ≤250 mm (10 in) annual precipitation. Temperature is irrelevant.
Antarctica's interior gets <50 mm/year (mostly snow); some valleys (McMurdo Dry Valleys) have seen no rain for 2 million years. So, by the correct climatic definition, the polar deserts dwarf the Sahara.