Seems pretty doubtful. Not only is there no physical evidence of a worldwide flood, but there's no reliable record of it happening. And by "reliable record" I mean some credible historical description other than the Bible.
That means that, if it happened, it happened before the beginning of recorded history (when people were using stone tools and the most ambitious boats were rafts or hollow logs). Somehow we're supposed to believe that a culture that hadn't even begun writing things down had developed shipbuilding to the point that one man's family could build a boat capable of holding samples of every living thing and riding out the greatest storm in human history.
But OK, set that aside for now. Even so, that means that that wooden vessel has sat exposed to the elements for at least 12,000 years (since we know that sites like Damascus have been continuously occupied for at least that long), and yet it is still recognizable as wood.
No, the only way anyone could believe something like that is if they really, really need to.