A straight up problem for all parties is the precise timing of the flood. The 4000-years-ago tradition for many creationists is grounded in the tracing of the recorded lineages. However, it is not possible to determine if there are families or generations not recorded in the biblical record. The ones that are there are recorded because of their importance to the story of humanity.
That said, it would seem unlikely that "millions" of years of history are unaccounted for, and I am not even trying to imply such a thing. Was the flood 4000 years ago, 5000, 9000, more?--I do not know. Was there a flood at all? I sincerely believe there was.
Someone asked above, "EAS, what would it take to disprove the ark to you?" What have you got?
IF someday it is genuinely discovered that Adam and Eve never existed and that evolution is the mechanism God used to create the planet over billions of years, then we would be forced to conclude that the creation account was intended as a parable instead of as history. How would that impact my faith? At one time, it would have been devastating. Today, I would shake my head at my lack of understanding as to how to read the first book of the Bible and the book of Romans and then continue in my faith that Jesus is the Creator, ruler, inheritor, and king of this universe. Jesus is the Christ, the Holy One, the Alpha and Omega. Without faith in Him, there is no salvation and no Christian faith at all. Saving faith is in Christ, not in creationism.