Will Fate Stay Night go down as one of the classics of anime 10 years from now?
It already basically is. The only people who complain about it are teenage children and fedorabeards trying to be contrarian.
You can post images of one of the fate mains and literally everybody knows right away what seires they come from. Not the case for whatever Q-Cup-autism-hooker was starring in Koani's McDoujins from a year ago.
Haruhi, Fullmetal Alchemist, Ouran, Black Lagoon, Welcome to the NHK, Death Note etc etc.
Sure Fate's an influential and ubiquitous franchise, but it's obvious none of its adapted anime are classic-worthy.
When it comes to VN adaptations, only Clannad and Higurashi really come to mind as classics. You could make a case for S;G but it's too soon to tell if it'll remain relevant or not.
We're not exactly in an age where "classics" appear, anime has been in full milk the NEETs mode since at least 2009.
F/Z might be considered a classic, SnK, NGNL, and SAO most definitely will be by normies as well.
Beyond that I can't think of anything.
OP asked about classics, /a/ really isn't going to be who decides on what is a "classic", no matter how strongly you feel about it.
Maybe as one of the most solid fap materials of highschool kids - probably a solid top5 eroge choice.
Much like how today, those who read the VN and fapped furiously to Saber when they were 14 now love the ufo adaptations.
Casuals are still talking about Code Geass TTGL to this day, I don't see even casuals talking about any of the shows you mentioned in, say, 5 years (well, maybe SAO if they keep milking it)
True, but I don't think they'll be talking about in the same way as Evangelion or even Madoka, it may be relevant and even popular but I don't think anybody will consider it a "classic"