Most games do send player locations to other players before they are visible. It's easier programming, it's less computationally intense, and most importantly, latency requires it. Especially in fast paced games, if you waited until a player is visible before sending his coordinates, there would be serious issues with perceived lag.
So yes, the info you are interested in is in there.
Getting at it is a different story. As Horror says, the data is likely to be encrypted. Most game protocols are these days and the Quake engines definitely were. If it is using network code based on the Quake engines, expect to also find Huffman encoding and delta encoding which will make it more difficult to program to.
Your best bet would be to disassemble the executable and dead listing it along with some active reversing using something like ollydbg. It wouldn't be easy, but I've done that sort of thing before... When I had that kind of time.