Popularity should have nothing to do with their feelings towards someone... if the girl is what he likes then he will ask her out.
I was never intimidated, but most of the real popular girls were more interested in being popular rather than finding a decent guy, so they were not not my style anyway.
I did like this one girl in high school and she thought she was to good for me... I shrugged it off and went out with one of her friends that did not have a chip on her shoulder. All of sudden she saw me in a different light. She came on to me at parties and it was like not a chance hoe. I was glad that I chose her friend instead of her!
Some guys are intimidated by all sorts of positive qualities in other people - popularity, intelligence, athleticism, beauty. Young guys are especially prone to shyness in that way. There are great young guys who lack the confidence to ask attractive girls for dates. If you know a guy like that, you may have to ask him yourself.
When I was less mature, asking a girl out was intimidating. Her being popular was irrelevant. If anything, they didn't appeal to me because they are unmistakably high-maintenance. But, typically, the nerdy guy will be intimidated by the popular girl and will not ask her out unless extraordinary circumstances make it convenient to do so; and even when that happens there is no guarantee.