The answer is no.

Researchers say the body has about three-million sweat glands and a person working out aggressively sweats out about 0.7-to-1.8-liters each hour. The factors that influence how long it would take you to run out of sweat are your size, physical fitness, and hydration level.

Environmental and exercise physiologist Lawrence Armstrong says he has proved that the body continues to sweat no matter how dehydrated it is. Armstrong explains that once the body's core temperature goes about 104-degrees and the body overheats the intenstines will discharge bacteria into the bloodstream and you will go into shock, but you will keep sweating. He says it's impossible to sweat all of the water out of the body, adding, "People don't shrivel up until they are dead." 

[Metro Metworks]