Yes capture-pane can send it either to stdout or to a buffer you can then save with save-buffer.
-------- Original message --------
From: James Jong <email@example.com>
Date: 30/04/2013 23:44 (GMT+00:00)
To: tmux-users <firstname.lastname@example.org>
Subject: Saving log so far to disk
Is there any way to have tmux save the scroll back (everything that has been printed so far on a pane) to a file?