Well, sort of. It reproduces at the same rate, there's just less to start with. I believe it doubles about every week. Persistence and consistency are the key. Every week or so, get out all you possibly can. In a few weeks, you'll have it under control, but I bet you'll never get rid of it.IME, the less you have in there the slower it will multiply.
Not so in my tank. I have an added powerhead in mine, and the duckweed still covers the top of my tank in just a few weeks if I slack on removing it.Silver Dollars eat them, but of course they'll eat your plants too. What I have found to be the best passive way of keeping them at bay is high surface water movement. Not agitation to degas the CO2, but just movement. Duckweed like stagnant water.