as long as multiple computers don't change the metadata of the same
image file at the same time, this is no problem. JPhotoTagger
installations on other computers having their separate own database but
do read the metadata of the sidecar files, so keywords etc. will be the
same on all computers reading the same files, e.g. via network.
JPhotoTagger - a Java application - is not aware of network drives, but
you can connect to a network through a drive letter or Junction. You can
change the metadata on the PC or the notebook: It will be written into
the sidecar files seen by all other computers. If JPhotoTagger on the
other computer does read the folder with changed metadata (XMP files)
and it will update it's (separate) database automatically.