So you want an answer do you? Hahahahahahah
:devil: Step into the dimension of the underworld! TO bring about the secrets! :devil:
Well to simply put, it depends on the coordination of the transmitter's periphrial vision, this case being Itachi.
What I'm saying is if a person is quick enough to move when Itachi closes his eyes, there out of the center of vision. However he can still see you with his periphrial vision, like the corner of his eye, so he can still activate his amaterasu and chase you at a concentrated and steady speed, to correctly catch up with your velocity at which you run.
So it's a 50/50. It's possible to dodge INSTANT activation of amaterasu, simply by escaping his attack range, but then it's also not too possible because Itachi's periphrial vision comes into play. He can look off the corner of his eye to see you, and instantly lock on and try to catch you.
~Spoken by the Dark Spire~