Pre-sale question: Buy specific product, choose one of four gifts

I need a condition where, when you buy a specific product, you can choose one of four products as a free gift. And though the paid product should be available in the WooCommerce store, the purchaser should not be able to see any of the “free” products in the store because they cannot be purchased. They are only available as a gift.

Will your plug-in accommodate that option? Thanks.