Assuming that an Earth analog was inhabited by both plants and animals like our Earth. Could the non-animal life on the planet survive the absence of animals (excluding sponges and corals) on the planet? Assume that all non-animal life (plants, fungi, bacteria) is unaffected and the animals were wiped out in an extremely short time frame (within weeks or months).
Some plants rely on animals for their life, therefore all these animal dependent plant would take a hit from the sudden disappearance of animals.
Think of reproduction: bees are the paradigm of animals helping some plants to reproduce. But there are also seeds which do not develop if they haven't been through the intestine of an animal.
But also think of gathering nutrients: animal feces are a significant part of the food chain. With no animal to spread their feces around, it could be more difficult for some nutrients to return into the food chain. This could affect some organisms, though in a less dramatic way than being unable to reproduce.
Could the non-animal life on the planet survive the absence of animals (excluding sponges and corals) on the planet?
Yes if they do not rely on animals for some part of their life cycle.
The sudden dissappearance of all animal life fom a planet would lead to a mass-extinction in plants as well.
As explained by L.Dutch, many plants rely on insects, birds or other animals for reproduction, especially all flowering plants. These wouldn't die as suddenly as the animals, but at the end of their natural life span, there wouldn't be enough seeds to grow a next generation.
The proverbial apple that doesn't fall too far from the stem would cause increased competition between a mother plant and its seedlings. The lack of animals carrying seeds far from the mother plant leads to crowding of same species plants, which makes them vulnerable to diseases. Some trees have such a dense canopy that seedlings cannot survive beneath them due to lack of sunlight.
Then there's the matter of the food chain. Many plants that can grow and reproduce very fast are the very bottom of a food chain and other plants that grow slower rely on animals eating their competitors. Once there are no herbivores, fast-growing plants like grass or seaweed would suppress slower plants by suffocating them or using up most nutrients.
Heath landscapes and bushland would be covered with trees because herbivores don't eat the soft buds of them and keep them short. Coral reefs would be suffocated in algae and seaweed. Grasslands and savannahs would suffocate under the dead grass of last year and a single lightning strike could set half a continent on fire.
Some plants would survive, but many would die, even if they don't rely on animals to survive.
Theoretically, the answer is "yes"
- Plants are thought to have evolved on Earth starting in the Proterozoic Eon.
- The first known footprints on land (not exactly animals, but close enough) are from the later Palaeozoic Era.
So, having evolved that way, it theoretically can return to that condition. However, the more you take from the existing ecosystem, the more difficult (and therefore less likely) it is the ecosystem will survive. Animals, probably. Animals + insects? Maybe not. Humans? Comedian George Carlin posited that the only reason humans evolved is because the Earth needed plastic. So it's probably safe to remove humans.