The first sentence clearly implies that he could be a successful person - for clarity the reader would need to see the context or you should add something, such as 'one day' or 'in time'. Now in the sentence as it stands there could be two meanings: either (1) there is some doubt as to whether he is successful or not, now at the present time or (2) the sentence could mean that perhaps in the future he will be successful (probably because already there is some indication of this). This second meaning is the more likely one to most readers.
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shininggirl"He could have been a successful person." has two meaningsDefinitely, but see the preceding posts for clarification. Maybe he was vs. Unfortunately he wasn't.