No. If you do this, customers won't be able to find first-hand information about your
products on Search, and there might still be third-party information for the product
that may be incorrect or incomplete. It's better to still allow that page, and mark it
out of stock. That way people can still understand what's going on, even if they can't
purchase the item. If you remove the product from Search, people don't know why it's gone.