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Obviously it does. This is at lueast, what the Dictionary of American Family Names, Oxford University Press says:

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http://www.ancestry.com/search/SurnamePage.aspx?sourcecode=13304&html=b&fn=&ln=Addison&submit.x=0&submit.y=0

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http://www.ancestry.com/search/SurnamePage.aspx?ln=McAdams&fn=&sourcecode=13304&html=b

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Well, you will find a lot of different surnames with the same meaning in one culture:
From the same word: Koller and Kähler (coal burner)
From different words meaning the same: Fiedler and Geiger (Fiddler)
In the case of Addison I think it's the Nickname Addie that created the variant.
Could this be an explanation?