Seems there are (at least) two components to this growth: earned income and unearned income. In other words, the income one gets from wages or business profits, vs. the returns one gets from passive investments. With the former, net worth grows more-or-less linearly (depending on how the underlying wage or business income grows). With the letter we get the more familiar compound return curve.
Percentage growth when net worth is ~$0 and growth is dominated by earned income is somewhat meaningless.
Percentage growth from unearned income will be driven by market performance in one's investments of choice.
MDM nailed it. Early on, when your portfolio is less than 5x annual income, savings has a substantial impact on NW growth. Eventually, around 10x income, compound growth on the portfolio dominates, and has been ~7% nominal historically. There is no 'saturation point' on this.
As a simplified example, let's say your income is 100k and you can save 50k. Up to 500k portfolio, you can see that the 50k savings added to the portfolio is a substantial boost. Eventually, around 1 million, 50k is less than the 7% you expect (on average) to return on your portfolio.
Of course, the real world has a few more twists and turns - sequence of returns, asset allocation, inflation / interest rates... But Thomas Pikety recently put forth the case that r>g (rate of growth on capital has historically been greater than rate of income growth), so, in other words, build up your portfolio and eventually it will take care of you (and your heirs) better than trying to increase your wage income. It also implies that the rich can indefinitely widen the gap between themselves and the working poor.