They don't provide FTP access to those files, but it is not impossible to get the log. I've slowly been working on a stats parser for Black Ops for my clan's website.
See here for my clan's BO server's games_mp.log: http://uancletus.com/bostats/?type=games&sid=554207
To get anything worth using, you would have to request the log every 5 minutes or so then compare it with the last data you got so that there isn't duplicate data.
If you are interested, PM me.