Interesting idea. You might have trouble with the TOS though. I'd have to read it over again, but I'm pretty sure it specifically forbids memory dumping the code, which is essentially what you are contemplating doing.
But let's ignore that for the moment.
Most likely, if I were guessing, I would suspect there is probably not a full on combat log stored anywhere in memory. What you will get from the server is a single line of text (one combat message), which will then be 'burned' into a texture, and that texture is what you are seeing on the screen. Once it's on the texture, you don't need it any more, and it's likely discarded. The texture itself is not going to be much use to you, so really what you need to do is catch that line of text as it is heading for the burning routine.
Of course, that is just speculation, I could be completely wrong. But if I were coding it, that's what I would do (eventually you have to put that text onto a texture to display it on the screen, and there is no reason to do that every frame, if you just burn it the one time you can save yourself a lot of CPU/GPU cycles).
So look for one line rather than a full log. And it may be compressed. Text is fairly easy to compress into smaller memory (which is good for sending in packets), and if so it won't be in a readable form that you would recognize from a memory dump. Of course, the compression/decompression routines involve extra overhead, so you might get lucky and it won't be. Depends on whether the devs thought the extra speed hit was worth the smaller packets or not.
So yeah, that's definitely the hard part. Once you get past that, then it's just statistics, no problems there. The packets themselves may even be timestamped for you, which would be a help (if not, you'd just have to assign a timestamp based on when you read them, slightly less accurate, but probably not a big deal). One oddity you'd have to possibly deal with is the (sometimes) strange ordering the combat logs come out in. Things like the death message appearing before the damage messages, things like that.
But, before you get too far into it, read over the TOS and make sure you won't get yourself into hot water, heh. Turbine got burned with seemingly harmless apps that memory dumped the Asheron's Call game that turned into all sorts of exploits, so they might be over-sensitive to such things now, I dunno.
"They laughed when I said I was going to be a comedian ... They're not laughing now." - Bob Monkhouse