Yes. You can turn on logging by adding the following INI setting:
make_log_file = yes
This lists all the files XMetaL Author opens and searches for each document opened or created. Listings include timestamps, DTD / Schemas and catalog files and brief descriptions about what is being searched for.
By default this file is created in the same folder as the xmetal60.exe. You can alter this location using the following INI setting:
log_file = <full path>
If you are looking for logging of some other kind we do not have anything else.