If you assign the sale to a collection and add the product to this collection, then the sale will be applied to the product automatically.
But there is one small nuance. If you added the product to the collection on the Edit Collection page and haven't made any other changes on the Collection page except for the products list update, then Shopify doesn't provide a webhook, and the app can't see the update.
So, if you added the product to the collection from the Edit Collection page, then there might be some delay before the sale is applied to the product in question. But the app will run the script, and the sale will automatically be applied to the newly added product without any additional steps.
If you want the sale to be applied instantly, you may add the product to the collection on the Edit Product page. In this case, the webhook is generated, and the app will apply the sale immediately.