This is the same argument so many YECs love to use; however, because they lack basic geologic knowledge, they don't realize that the sediment that presently makes up the geologic column had to come from somewhere. It had to have been eroded.
The most productive way to create sediment from erosion is to erode highlands, otherwise, you're just moving dirt around. In other words, you need to erode land that is above sea level and the higher the better. The higher the land, the better the erosion, and the greater the amount of sediment available for transport and subsequent deposition (i.e., the geologic column).
If the pre-flood land was "relatively smooth," then erosion will be relatively non-productive.
Let's think about this logically, Buz.
Let's say you have a land mass that is relatively smooth. What's that? Maximum 2000' high rolling hills? Then the rains started. Since all the land masses were covered by water, that means sea levels were raised globally. That's a LOT of rain.
So what we have is rain that is simultaneously eroding the hills and raising sea levels. The more you raise the sea level, the less erosion you will have, and therefore less sediment (remember, the higher, the better). In addition, the rising sea level is covering more and more land, which prevents it from being eroded. The longer it rains, the less sediment your model produces. Your model results in far too little sediment production and not very much water.
All you'd see in the geologic record is oceanic crust overlain by oceanic sediments, which would in turn be overlain by a very thin cover of continentally-derived sediment that is graded from thickest at the bottom to clay at the top. This continental cover would be traced across the entire globe and you'd be able to follow it from the ocean basins up onto the continents - on each and every continent. The sediments would be thickest at the continental margins and pinch out both towards the deep ocean basins and possibly on the land if the land masses still had any topography.
On the land masses themselves you might see peneplanation of the hard rocks and sediment-filled basins, and a generally flat landscape. However, hard rocks don't necessarily erode very easily in a few days of hard rain. They erode much better with time. Time allows water to seep into the rocks, alter the minerals to softer more erodable material such as clay. Transport in streams, not getting hit by raindrops, is what transforms boulders, cobbles, pebbles into sand.
I'd say you'd have to have a virtual lack of hard rocks in your model, which means no igneous rocks and very little in the way of metamorphic rocks.
It doesn't work, Buz. Even with my simplistic and totally non-technical examination of your model, your "relatively smooth" pre-flood earth would not produce enough sediment to result in the geologic column, nor enough water to depress the oceanic basins.
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