Yes - they CAN both use the same library. Calibre always assumes a path relative to the library folder.
What you must NOT do is have Calibre running on both machines at the same time. This is almost certain to result in the Calibre database metadata.db file getting out-of-sync with the actual books.
There is no automatic "watch this folder" feature in Calibre for adding books, although I believe that people have built their own custom system based on the Calibre Command Line tools.
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