Can my shop have products that are not fulfilled by Printful?
Yes, of course! Both classes of products can coexist in one shop. The only disadvantages are: 1) If you're using Shopify, you can't use the "override shipping settings" feature. This is because we would not be able to return the correct shipping rates if your customer's cart contained both Printful and non-Printful items. 2) If you're using WooCommerce, you can't use our shipping plugin for the same reason.
If you offer both classes of products on your store (regardless of ecommerce platform), Printful will only fulfill the products that are synced with Printful. After the product has been shipped, Printful only updates the shipping status and provides the tracking number (for those platforms which allow it) for the items that were fulfilled by Printful.