@Troy what do u mean by "incomplete (for example if you have a pending trade-in or if you are not paying cash) and your edit button disappears"?
If on your order page, you filled in all the requested information (address, license, insurance, payment info etc) then it means the order is complete from your end. All you have to do now is wait for VIN and delivery. If you completely filled in these details, the edit-design link disappears. In this case the disappearance does not necessarily imply anything.
If you are financing (via tesla or any other 3rd party/credit-union) as opposed to paying in cash then you will have to leave the payment section incomplete as you need a VIN to get a formal loan etc. Similarly, if you are trading-in your existing vehicle then you will have to leave this section empty as well until Tesla processes your trade-in which happens only after you are assigned a VIN. If in this case, the edit-design link disappears, it means that you have a VIN assigned and you cannot edit your order anymore. There is a chance that the said VIN might not yet appear on your order page though.
I am in the 2nd bucket. I don't have a trade-in but I am financing my purchase. So I left that section incomplete (i.e. no green checkmark, but three grey dots). As you can see in the image below, my edit-design link is still present and I can click and edit my config, meaning I don't have a VIN assigned (
)!
One more indication of VIN assignment (other than the edit-design link disappearing) is that grey dots next to your incomplete sections would change to yellow!