No. Wishpicks doesn't send your wishlists to Google. An Anyone with the link or Invite only wishlist is never indexed by search engines, so it won't turn up in Google results.
How each visibility setting behaves
Anyone with the link (the default) — Not indexed by search engines, not listed on your profile, and not browsable. People can only open it if you share the link with them.
Invite only — Not indexed either. Only you and the people you invite can see it. Everyone else gets a "No Access" page, and even the link preview is hidden.
Public — Shows on your public profile, so someone who has your profile link can reach it from there. It still isn't placed in any browse, feed, or search surface on Wishpicks.
Why it works this way
Your public profile lives at a handle like /@yourname. We tag profile pages to ask search engines not to index them, but a search engine can still crawl a page it finds linked somewhere else. To keep a list off your profile, set it to Anyone with the link or Invite only instead of Public.
Sharing a link in a public place (a forum, a social post, a group chat that's indexed) is what usually makes a list findable — not Wishpicks. Where you paste the link is up to you.
Changing a list from Public to Anyone with the link or Invite only takes it off your profile right away. A search engine that already cached the page may take its own time to drop it, and that part is out of our hands.
There's no "make my whole profile private" switch. You set visibility per wishlist, so you control discoverability one list at a time.
Related
Who can see my wishlist?
How to make a wishlist private
What information is visible to guests?