This file is stored on a network server, however. I was wondering if windows has any way of marking the file as to which computer it was saved from on the network.
No, it just saves the general info in the file, user that created it (if setup in Office), file type, date of creation, etc..
If you have auditing turned on in the server, you may be able to see which user placed the file there, and possibly which PC it came from. Just the file itself though won't tell you what computer it came from.