Can someone survive without saliva?

No. Saliva is definitely needed for the general health of teeth , gums , tongue and oral tissues in general. If you have a dry mouth there are several products on the market for that like biotene and aim artificial saliva .
Yes, but... Not producing saliva may be a sign of a greater disease process, and should be thoroughly evaluated by a physician. The greatest concern is a rapid increase in dental caries (cavities), and so a mouth rinse may be used as a substitution. Certain digestive enzymes begin with salivary breakdown of foods and is a part of the digestive process as well. Call your M.D.