Is there a way I can create draft orders
1) Admin will create the order
2) Add the products
3) Add the billing/shipping info
4) Create the order
5) Customer gets notify via email
6) Customer login and pay for the order?
For your requirement you can do the following things, so you can achieve that one.
1. Use Magento Default Order Process like Select Customer, Added Product To Cart, Select Billing and Shipping Information. (This is already added product to customer cart).
2. Now Create Custom Button, by clicking then it will send email to customer, into that customer able to see the product and all from the cart.
3. Now on same email you can place "Checkout" Button at the last.
4. Now from that button, put the custom URL link and pass the cart id, so one's customer click from the email, your custom URL call where you get cart information and you can restore that cart programetically and redirect customer to cart page.
5. Now Customer can pay same like default checkout steps.