Quite honestly... I don't know the answer, and I have not seen an robust answer with my own two eyes.
Masanobu fukuoka relied of seeds in clay pellets in his system to reduce bird predation. He did that work but little else. It might depend on the species of plant, and how long you run the animals. Perhaps you might do some kind of animal treatment after 2-3 years, when perennial weeds become stronger? I have gotten a couple of years of kale to regrow, and my garden beds sprout from the seed bank, but eventually the grasses get strong, for me particularly Agrostis stolonifera.
I can't imagine that the chickens would destroy ALL the seeds, and a wild seeding is often to dense for good leaf production, so some thinning of the seed bank might be useful. I have one patch where I am trying to load the seed bank with vegetable seeds, but I run chickens and dump in mulch in winter, and do some spot tillage for the tough weeds. I am hoping to feed myself in spring and summer, and then running the chickens in fall or winter while leaving a vegetable seed crop to mature above chicken height. It hasn't worked well yet.

But I see enough success to know it is possible.
For small plots, another type of disturbance could be mulch. In a school plot I just looked under the standing waste of lupine, and found lots of lupine seedlings germinating early in that protected environment. I don't know if they would be doing so well if I had cleared the bed rather than leaving the debris.