I'm not sure that even the pro-Nostraticists argue that it's the proto-language. I guess it boils down to whether you think Neanderthal spoke or not. You're probably better off asking a pro-Nostraticist than me. There is a book called Nostratic: Sifting the Evidence edited by Joe Salmons, that I've been meaning to read. (And the Russian linguist whose name I was trying to remember earlier in this thread is Vitalij V. Shevoroshkin.)