No. Not only did he earn it, but having his dad pay his way all his life is only going to turn him into a spoiled brat.
Personally I think it's nice to see that he's taking control of his life and working hard, something you don't see many celebrities do.
The fact that this is an issue is disgusting. It's like if he got a job, people would be saying "He doesn't deserve to get that job! He shouldn't be able to work for his money, because his dad already has money, he doesn't need it!"
Reminds me of the occupy wall street issue. If somebody earns the money, they earned the money, rich or poor.