They grow exponentially, yes, but they'll stop reproducing when the store of sterols/lipids they started out with - and which is not replenished - runs out, or rather reaches a critical level, even if there is fermentable sugar left. Then they start the hibernating process. So it is wrong to presuppose that they will just go on reproducing till they've compensated for the low number pitched. This is my issue with the Shaken, Not Stirred method. No matter how healthy your yeast is, you can't ignore the need for a certain population size.
A quotation from dr. Clayton Cone of Danstar: "At each doubling it will split the lipids with out making more lipids (no O2). The first split leaves 2.5% for each daughter cell. The second split leaves 1.25% for each daughter cell. The next split leaves 0.63%. This is the low level that stops yeast multiplication. Unless you add O2 the reproduction will stop." (The source for this not available any more. I've got it from a Norwegian blog.)
The rest of what you say here, is pure Truth
.