No. The content taught by the degrees might be the same but some university open more doors for you and definitely put you ahead of other students simply because of the prestige attached to their name.
It's not really that big of a deal honestly unless you aim for the moon. How many people do though? Most people are average joes with no dreams of grandeur.
My mom, her only worry was that I end up jobless, homeless. She would have been fine with me working at Walmart.