Simple answer: Yes. Most of the time.
Not-So-Simple answer: Yes, if there's no control on their growth.
For example, I have a heavily planted 30T with lots of fishes. This tank has minimal tech support, only a pair of air-driven floss-box filters and a set of strong lights on timers. Aside from plant-specific substrate and fish wastes, there's no added fertilizers. The concept behind this tank is a mostly self-sustaining tank with minimum gear attached to it. The plant, and to a lesser extent the micro-fauna, provides the filtration to eliminate animal wastes. The filters are there only to provide water flow and remove the larger particle (only for aesthetic reasons).
I don't have too much duckweed problem (so far, lol). I think that's due to several factors:
1) The water flow from the two filter box goes up the rear corners then to the front's center region. This flow pushes the duckweeds and other floating plants to the front. This means that they are no longer directly under the lights, which is located across the rear of the tank's top. Incidentally, this also clears about half of the water surface, this helps gas exchange which probably mostly occurs in the rear corner areas, where most of the surface agitation is.
2) The tank is also tightly sealed and it's heated to about 78degF, the airspace (4"H) in the top of the tank is actually quite humid. I actually have condensation running down the inside glass surfaces. Correct me if I'm wrong but I've heard that duckweeds prefer slightly cooler and not as humid environment? If so, that'd be a factor too.
3) As for the plants being consumed by the fishes. Considering the species in the tank I think, at least for this tank, it's not a factor. I currently have 22 Glass Bloodfin tetras, 18 Gold Neon tetras, 3 otos, 1 ringed loach, and about a dozen glass shrimps. None of which are plant eaters, with the possible exception of the otos, but they seem to prefer working on the plants and glass sides. The glass shrimp seems more interested in the detritus along bottom rather than swim nearly 2' to top of tank for duckweeds.
Yes, I know that's VERY heavy fish load, even for a 30T, but this tank's an experiment based on an 'impossible' tank setup I've read in a major fish magazine. This tank had nearly 40 fishes of various types (barbs, rasboras, tetras, loaches, otos) in addition to lots of shrimps. The idea is to have a balanced tank with minimal equipment that is mostly self-sustaining (feeding once every few days).
Btw, I plan to rehome the neons to a 16T tank, mainly due to a different unforseen problem. I love the sight of a large school of fishes keeping to a tight pack. However, I've noticed that while the glass bloodfins was schooling nicely and likewise the gold neons, when put in the same tank, they tend to mix up and spread out almost randomly. I'm going to set up a similar tank setup for the neons (complete with duckweeds too, i suspect).
For your information, my tank started out with 5 sword plants (not sure which species, but I got them for cheap at, of all places, Walmart), 2 E. vesuvius (actually now Helanthium vesuvius), 2 E. tenellus (again, Helanthium tenellus), 2 Sagittarius terres, 2 S. spp (unidentified specific species, but it's definitely a sag). Yes, the planted tank is also a SA tank too.
Now the 5 swords are all larger (leaf-countwise), H. vesuvius is growing runners like crazy, both sags are also shooting runners. Initially I thought I was going to lose the two H. tenellus, since the leaves were dying and both was down to 1 or no green leaves left. Recently noticed the 1 leaf on one seems to be recovering from it's damage in-transit plus new roots are forming out of the rosette. The other appeared dead until, of all thing, a runner poked out of the mass and started growing out to the side. I just picked up a bucket full of Cabomba carolinianas and will be planting them along the back of the tank tomorrow.
Hmm, gotten carried away again. Gnite y'all.