Depends on the network. The issue is that Word does not simply read the file
when you open it and write it back when you save it. On opening, Word
creates a lock file, optionally a backup copy, and a temporary work file
containing the moment-to-moment version of the document as you edit it. This
work file is read and written continually while you edit the document. Then
it all gets cleaned up when you save and close. All of which makes for a) a
lot of network traffic, and b) non-trivial file activities.
Which is why saving across the Internet is fraught, and why working with a
document on a removable medium is deadly. On a simple, low-volume
peer-to-peer network you will probably be OK. But why gamble? Silly to risk
losing your Word efforts because the person on the other machine picks a bad
moment to bring the network to a halt by restarting their machine or
downloading a remix of In a Gadda da Vida.