But I've never seen them actually ingest any. Silk plants are great. My birds spend as much time in the silk plants as the live ones. They don't need water, fertilizer or sun, and are easily cleaned. The important thing is that they provide good cover.
Many live plants are OK in aviaries.
The type of birds you keep will help determine which plants do well. In my aviary, I've had good luck with ficus benjamina, bottlebrush tree, bay laurel, bamboo, queen palms, and some ferns. Plants my birds love, and destroy very quickly, include pyracantha, podocarpus, spider plant, bougainvillea, and various pines and junipers. The European goldfinches love the growing tips of the conifers. Every finch I have loves pyracantha.