Bro jl,
I do believe, as well as every solid Christian (in my eyes, of course) I have asked or heard from, that demons come from the fallen angels of Genesis 6.
I am undecided/unclear about whether they were one and the same (or in part) as the Nephilim and/or giants that the Israelites destroyed (the theory that the demons had bodies (half-fallen angel/half-human) and were disembodied upon their death). I haven't heard a Scripture that would completely validate or unvalidate the idea. I think only the fallen angels that chose wives created giants, while most fallen angels chose to inhabit human bodies (possess). Any possibility brings up questions we can't answer from Scripture.
Yes, the theory you are talking about, the fall of Satan prior to the creation of the garden, I have heard it called the Pre-Adamite rebellion, and it does assume either the Gap Theory or the Day-Age Theory (each creation day represents a larger period of time). The reason that it is un-Scriptural is that Ezekiel states that Satan was 'perfect' in the garden of God until iniquity was found in him. Genesis says that everything was good when God created it. Satan and the angels must have fallen after the creation of the garden, and after everything was 'good'.
If you, however, don't believe that Isaiah 14 and Ezekiel 28 refer to Satan, then there is no real evidence (that I have heard of) that supports or negates the pre-Adamite fall/rebellion.
If one's theory is that the fallen angels are not the demons we encounter today, then I would be interested to hear (from that viewpoint):
1) the origin of demons
2) the definition of Satan's angels Matt 25:41 / Rev 12:9
3) the difference in demons and the angels reserved in chains from Jude 1:6-
And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day