If we treat the 5V line as being at 0 when 12V is first applied (discharged cap capacitance) then current of 12V/1000 = 12mA can flow. As the capacitance charges up, current will drop, and if the equivalent load becomes another 1K, then Vcc wil become 6V and current will drop to 6mA.
A Nano has the 328P, FT232, Power LED, and the Rx/Tx LEDs driven by the FT232. What equivalent load would those all represent?
Say only 500 ohm. Then current of 12V/(1000 + 500) = 8mA would flow, 8V across the 1K and 4V across the rest.
Say the load was higher - 2000 ohm.
12V(1000+2000) = 4mA, 4V across the 1Kand 8V across the rest.
The 328P and FT232 are active loads tho, I don't know what their equivalent static load would be, or if 8V into Vcc while the 328P is attempting to boot up would damage it.