Yes, it appears possible as long as both computers can access the same catalog file and the photo files on the NAS or shared storage. Community responses note that earlier Photoshop Elements setups could use a single catalog on external/shared storage, so PSE 13 should work similarly.

The main limitation is performance and practical use: network access, especially over Wi‑Fi, can be too slow for comfortable day-to-day use. A wired network connection is more likely to be usable.

A sensible expectation is that the catalog can be shared between computers, but not used simultaneously by both at the same time. Also make sure file paths and permissions are consistent so both systems can see the catalog and images correctly.