It is uncertain when Satan and the rebellious Angels rebelled against God or even how far the war had progressed before Satan and his Angels were ejected from Heaven.
According to Scriptures which is the basis for Pink's analogy.
Genesis 1:1 In the beginning God created the heaven and the earth.
is simply a statement that God was the creator and:
Genesis 1:2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
is descriptive of his creation at that time.
Pink apparently deduced from:
Luke 10:18 And he said unto them, I beheld Satan as lightning fall from heaven.
Revelation 12:9 And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceiveth the whole world: he was cast out into the earth, and his angels were cast out with him.
That since Revelation says that he was cast into the Earth it had to be without form and void.
This would make more sense if as; some believe, that the Earth was created at the time of their being expelled from Heaven as a place of interment for Satan and his Angels. This also gives more meaning to the bottomless pit also spoken of in the Revelation.
As far as the gap theory goes it's basis in not between Genesis 1:1 and 2, but between verses 1 and 3, and some validity for this theory lies in:
Genesis 1:5 And God called the light Day, and *the darkness he called Night. And the evening and the morning were the first day.
The darkness referred to in verse 5 can only be eternity preceding the creation of light, since God starts that first day with darkness, with the light being the second part of day one. This also gives reason to debate the 24 hour day theory for the creation, since the 24 hour day is based on the cycle of sunlight and darkness which does not come into play until:
Genesis 1:16 And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.
This is of course depending upon whether or not Genesis chapter one is chronological, as you have stated in your question. The answer to that can only come from the numerology, that being that God divided his work of the Creation into days and broke it into successive numbers 1,2, and so on. The only logical reason for this is to delineate Chronology.
I can only give you the logic behind my answer to your question, you will have to determine for yourself what you choose to believe, since this is the most concrete evidence I know of and even that is subject to individual interpretation.
Hope this helps.