No. Nada works exclusively on collection pages, it moves sold-out products to the bottom of a collection, or hides them from the collection entirely. It does not affect the order of results on your store's search page.
Why does a product disappear from search?
If a sold-out product is no longer appearing in your store's search results, this is controlled by Shopify's own search system (or your theme's search plugin), not by Nada. Shopify's predictive search and search results pages have their own logic, products that are low in inventory or out of stock may rank lower or be filtered out depending on your theme settings.
If you want to investigate this further, check:
Your theme's search settings (some themes have a "Hide out-of-stock products from search" toggle).
What if I enabled Hiding and the product is gone entirely?
If you've turned on Nada's Hiding feature, sold-out products are unpublished from your Online Store. An unpublished product won't appear in search results because it's not visible on the storefront at all, that's by design. When it comes back in stock, Nada will republish it and it will reappear in search.