What material is Note II screen I made a little bit of research and I didn't find anything conclusive.

It is not listed in Gorilla Glass list. But somewhere I found its screen is glass, but someone else reported he scratched its screen keeping the device in his pocket without protection.

From a practical point of view how easily will the screen get any scratch if no protection film or case is used?
Due to a disclosure agreement, Corning (who make about 90% of screens) will not answer any questions on what devices use their technology. However, Samsung have said: "GT-N7100 does not have Gorilla Glass 2. Thank you for your interest."  

That doesn't say who makes it or what type of material it is I'm afraid. However, from friends and others I would say get a screen protector, it is MORE scratch prone than say the S4 (G Glass 3) but not more than the average device. Just remember the screen is BIG and that gives it more leverage if it is in a tight pocket / bag and is likely to have more force on it in these situations.

I'll keep looking and update if I find out!