No. Wishpicks doesn't send back-in-stock or restock alerts. Price tracking watches for price drops only, and an item that's sold out won't trigger an alert.
What Wishpicks does instead
Wishpicks tracks price drops, not stock. Alerts fire when a tracked price falls, never when a sold-out item comes back, and an item that's currently sold out is skipped entirely — no email even if its listed price changes. See "How do price-drop alerts work, and how often are prices checked?"
You can still see where things stand. A wish shows whether the item is available right now, so opening your wishlist tells you.
Worth knowing
A workaround: add the item to a wishlist anyway and open it now and then to check availability. There's no automatic ping when it returns.
Wishpicks isn't a shop. It links out to the store, so the store's own page is the source of truth for whether something's in stock.
Price tracking is separate. If you're on Wishpicks Plus, your tracked items still watch for price drops — that part keeps working. See "What is Wishpicks Plus, and what do you get?"