Does Pareto-efficency take into account growth?
It seems to me that as long as every person likes wealth any allocation $W_t$ will be Pareto-optimal.

Even if this was not the case, so supposing that $w_1, w_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.

So no, it does not follow from your conditions that $D_t$ necessarily equals $D_{t+1}$.