If you don't own Summerset, you will be unable to interact with the Jewelry Crafting stations.
You can still pick up the nodes in overland, but you won't be able to refine the materials, but you can sell them in guild stores.
trackdemon5512 wrote: »Addendum: If you are accessing Summerset through ESO+ without outright purchasing the expansion, you will lose the ability to interact with jewelry stations if your subscription lapses. This will occur even if you get your jewelry certification. Unlike other skill lines, jewelry is totally dependent on having access to the island.