Not likely at all.
If you read the back of a Red Sox ticket (or any MLB ticket for that matter) not only does it warn you specifically about objects leaving the field, by entering the ballpark and sitting down you assume responsibility and indemnify the team against damages.
I don't know about anyone else but when I go to Fenway and sit that close, I watch the game very intently.
It would be wise for the Sox to pony up the money anyway. A creative lawyer can find aw ay around the print on the ticket, and the bad publicity isn’t worth it.