The batch script only logs the calls to it so, in other words, you can see what script you ran on what drawings. That script does not capture the output of the accoreconsole session.
You can build a script (aka: simple lisp) to grab the information you want and write--append--to a common log file of your choosing. Accoreconsole allows you to open files for reading and writing to.
;; read
(open "C:\\Temp\\MyFile.txt" "R") )
;; write
(open "C:\\Temp\\MyFile.txt" "a") )
Typically I used that script to "clean" drawings that were to be sent off somewhere (client, for example). I kept a "job list" of files (it was another batch script that listed my project drawings) in my directory that when the time I just double clicked to clean all my drawings and it would call the accooreconsole batch script thing I made for all my drawings and the correct script (I had MANY scripts that did all sorts of things, like update titleblock info, plot, clean, make slide files, etc.).
@echo off
set SCRIPT="%~dp0\job-filelist_script.scr"
set logfile="%~dp0\scripting.log"
set FILELIST=
set FILELIST=%FILELIST%;"C:\Temp\FILE-001.dwg"
set FILELIST=%FILELIST%;"C:\Temp\FILE-002.dwg"
call C:\some\location\to\BatchDrawings_accoreconsole.bat %FILELIST%
So, you can create a lisp to grab the information you want from the titleblock. Use the `job list` method (most likely not what you want here), drag and drop, or even assemble the list of drawings from AutoCAD and run through them with my script thing to append a log for each drawing.