You do not have to add the product to Shopify (or another store) to sell it. Add to store is only for the connected catalog.
Manual / bulk
Go to Products → Bulk Orders (also under Orders). That page is a manual order to a USA address.
Approved custom products show toward the bottom of the list, by custom label ID#. Pick that row so the order uses your label, not the unlabeled catalog bag.
Only Approved custom products appear. Pending and rejected do not. 2oz custom rows are not on this list — samples / 2oz have a different path.
A store connection is not required for this page. You still need a payment method in Dripshipper Settings.
Store dropship
For checkout on your site, the badge must be Approved, then Add to store on My Custom Products. 2oz still has no Add to store.