You bring up a very interesting point. The instrument cluster receives a "Keep Alive" voltage whenever the battery is connected. Typically there is a processor, rom with firmware, some kind of a bus controller IC, and tons of other surface mount components. During a CRANK-TO-START, the electronics are still up and running, processing code, and communicating to the bus, and then when you let off the key will then receive all of the data from the communication bus to be displayed.
The electronics are designed to fully operate on less than 12.6 vdc, usually as low as 8 or 9v. No need to wait for the bulb check or needle sweep.
Where this can be a problem however is with poor engineering. Take a 30ft RV for example with a rear pusher engine. Recently a friend had one of these with long bus data line, and a long power feed to the dash that also fed a bunch of other stuff. Not only were communications over the bus being degraded by the long runs of wire, but whenever a CRANK-TO-START was initiated, the voltage wpuld fall to below 6 vdc even with perfect batteries. This kept corrupting the firmware on the instrument cluster and sever warranty units were swapped in. After a year of messing with it, they finally fixed the wiring issues so that subsiqent failers stopped.