I would assume it would stay at 4000 as on Bulbapedia's Egg page it makes no mention of this mechanic and this would be a something definitely worthy of mention if it did reset.
Especially considering they did mention something about eggs and trading in the Trivia:
Another issue with traded Eggs appears in all generations since Generation III: When an Egg is generated, it is given the OT, ID, secret ID, and game identifier of the game which created it. This can cause an Egg which is traded to hatch Shiny and then be normally colored, or hatch normally colored, and then be Shiny. This is due to the change in OT, ID, and secret ID happening after the hatching cutscene.
So also considering the OT, and ID remain the same one can assume that it would stay the same as well. Feel free to test it out though, you can run around so it says in the summary "maybe close to hatching" and then trade it too see if it is back to "It does not seem close to hatching".