Yes. On Wishpicks a registry is a normal wishlist that you've tagged with an occasion. There's no separate registry product to set up. Make a wishlist, tell it what the occasion is, add the gifts you'd love, and share the link. An event date is optional.
Steps
Create a wishlist for the occasion. See "How to create your first wishlist".
Tag it with an occasion: a birthday, a wedding, a new baby, a housewarming. On a new wishlist there's a picker on the empty list, and you can set or change it anytime in Settings → Occasion. The occasion is what powers your gift ideas.
Set who it's for, if you like. Open Who's it for? to add an age band and gender so the suggestions fit the person you're shopping for.
Add the gifts you want by pasting product links from any store, searching inside Wishpicks, or tapping Explore gift ideas. See "How to add a wish to your wishlist".
Add an event date, if you like. Turn on Link to event in the same Occasion tab and pick a date, or set one inline on the wishlist header.
Share the link with your guests so they can view the list and Reserve the gifts they plan to give. See "How to share your wishlist with friends and family".
Good to know
A registry is still a regular wishlist. Tagging it doesn't create a separate wedding or baby-registry object, and there's no completion percentage.
Once a wishlist is tagged, its empty state shows Ideas to get you started and an Explore gift ideas button with suggestions built around the occasion, and around Who's it for? if you set it. Those suggestions appear only where AI search is available in your region. Tagging works everywhere.
The event date does one thing: it lets Wishpicks email you a reminder about 14 days beforehand. Without a date, the wishlist's creation date is used instead. To stop those reminders, turn off Event reminders in Settings → Notifications, or use the Unsubscribe link at the bottom of one.
Reserving keeps the surprise. By default you won't see which gifts your guests have reserved, and the same gift can't be reserved twice. See "How does gift reservation work?".
There's no shipping-address field, so arrange where gifts go privately with your guests. See "Do I need to add my address to my wishlist?".
Two things a registry won't do. It won't split the cost of one gift between several people, since guests reserve a whole item. And it won't handle the buying: each wish links out to the store that sells it. See "Does Wishpicks sell products?".