If orders are coming in as a "Paid" status and our Integration App says "Authorized", would both be imported?
Yes, this is due to the current design of the Integration App. When a user selects the setting as "Authorized", the Integration App allows an order import for any of the orders with the financial status of Authorized or Paid.
This is due to the fact that if a user has set their Shopify account to "manual capture of payment" then orders placed via the storefront would have a financial status of Authorized. On the other hand, a merchant can place an order through the admin panel directly in a Paid status. Considering the practical use case that the merchant would want orders to be imported in both the scenarios, the Integration App allows the "Paid" financial status orders as well.