Answer:
False
Step-by-step explanation:
Delaware is a small state that holds over 1 million companies, over 50% of all publicly traded corporations in the US and more than 300 of the Fortune 500 corporations. Basically, many companies incorporate there for the tax and legal advantages that it offers.
But Delaware, as well as every single state + Washington DC, requires that all companies registered there must have a registered agent that lives within the state. It doesn't matter if the company does or doesn't do business in Delaware, or any other specific state, that is legal requirement.
In a place like Delaware, it is probably a career to be a registered agent for foreign companies, since there are more companies than people.