[original post removed]
Not necessarily.
FCFE = NI - (1-DR)*(FCInv - Dep) - (1-DR)*(WCInv)
Dividend = NI*(Payout ratio)
Assume that the Payout ratio is constant, then a change in NI is the only factor that affects the dividend payment, which means the percentage growth in NI is equal to the percentage growth in Dividend.
Div(1) / D(0) = NI(1) / NI(0)
Now if the growth in FCFE is equal to the growth in Div, it is also equal to the growth in NI. But FCFE has other terms in the equation besides NI, so the result will only hold if the growth in the other terms is also equal to the growth in NI.