I think it would have because Simba did flinch in pain after Zazu plucked the strand out. After all hair is hair regardless of length and therefore the pain level should be indifferent even if it's a full grown mane. I know I tend to feel pain when somebody pulls on my hair when they're styling it. So yes I can imagine that it did hurt.
It probably hurt, but not too much. It was only one hair, after all, and I think we all had a hair pulled out either on purpose or by accident, but I doubt it was anything any of us cried about.