I do want to say that I’m not intentionally trying to be vague. I apologize if it is coming across that way.
To remove all doubt, the most direct answer is No
Use Shopify checkout.
Shopify can’t guarantee the safety or security of an order that’s been placed through an offsite or third party checkout. Apps that bypass checkout or payment processing, or register any transactions through the Shopify API in connection with such activity, are prohibited.
I can think of some cases for offline orders where merchants could benefit by having an app that can import this for them to complete the fulfillment. I will pass that on to our app store team as a feature request to consider for future updates to the requirements.
Currently this is possible in the admin, Shopify POS and in the Shopify Mobile app for customers needing this functionality right away.
Once the order is in the admin, we do have some guidance here on order and fulfillment management apps on managing 3rd party orders: Track orders placed on other platforms