In speaking to someone from Tesla today, the process seems to be that you put in your order, and list your trade-in with photos etc.
The trade-in valuation is done once a vehicle is assigned to your order - but the absence of a valuation does not delay getting a vehicle assigned to you. This gives me the impression that not putting in a trade-in, or taking one out when one is in there as "pending" would not speed up the assignment of a vehicle to you.
Once a vehicle is assigned - and assuming the above is true, then I suspect a flag is thrown internally and your trade-in is assessed, and an offer is made.
In speaking to Sydney Tesla today, and in referencing my particular order (details in sig together with order and amendment date), the expectation was that we would have a vehicle around mid September. Frankly, I am surprised by this, as I would have thought delivery and unloading would take around 4 weeks from Shanghai? In other words, a vehicle would need to be allocated in the next fortnight to my order to match that time frame (if I am right on shipping time), yet others above have no VIN despite ordering weeks ahead of my order...
Make of all this what you will, simply passing on what I was told today