Do the enzymes and compounds in saliva help with stain removal?
It would depend on the stain - and more specifically the material and staining agent. Saliva contains blood clotting agents so I doubt it would help with removing blood stains. The enzymes in saliva are unlikely to help with the stain removal. 

The water in saliva would be more likely to help, dissolving the stain. So your probably better off with water.