That depends on whether the version of Ethical Egoism you're talking about is sophisticated or naive. Suppose an ethical egoist realizes that he will be most happy if he has nourishing, intimate relationships, and is able to pursue his ends in cooperation with others. Suppose, further, that he thereby endeavors to cultivate within himself certain virtues, such as honesty and compassion (because they are necessary pre-conditions for achieving the goods above). This sophisticated egoist may indeed have a healthy personality, even though the ultimate reason he develops such a personality is to pursue his self-interest.