Its certainly possible because it happened (your signatures appear to be authentic based on examples I have and others I have seen such as Bill James printing his signature on a Baseball which I have seen before).
If I were you I would check around and see if perhaps the Braves played the Red Sox in an exhibition game that year. If not your theory of having an American League Baseball available at Fenway is certainly possible.
Its a nice pickup and more historically significant than valuable because "signed" baseball sfrom this era basically dont exist. This is about number 40 or 50 I have ever seen in 20+ years of collecting from the entire pre-WWI period.
Rhys
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