No, Tennessee does not have any true deserts. The state's climate is humid subtropical (most) and oceanic/humid continental (high elevations), with abundant precipitation (1,000–1,600 mm/year) and lush vegetation.
However, localized, temporary arid conditions can occur:
These are microclimates or weather events, not desert biomes. True deserts require <250 mm annual precipitation; Tennessee's driest areas get >1,000 mm.