It can go on the external. Both my DAZ and Poser installs are.
The basic libraries for modern versions of DAZ Studio (and I think Poser) can be wherever you want. All you have to do is tell Studio where the library roots are. However, I seem to remember problems with the DAZ Studio3 version of the “Category” index not being portable because it seemed to remember which letter-drive the items were stored on. I remember someone posting a very long and complicated procedure on how to edit the category index to fix that problem but for me it was more trouble than it was worth. I simply gave up, erased my Category index and manually re-categorized everything (which I’d thought about doing anyway). Took me a month. :-(
Perhaps the DAZ Studio4 content manager is smarter about automatically re-identifying where your library items are but I sincerely doubt it.