Yes, plants live in all but the most exteme of deserts such as the Antarctic where few plants live and are rare in the Atacama Desert.
By definition, in the desert
There is a surprisingly large number of plants that are able to survive in the desert and few of them are cacti. Trees, shrubs, grasses, perennials, annuals and even some ferns and mosses can live in the desert.
Plants that live in the desert have long roots so when it DOES rain they are able to gather a lot of it. They also have small leaves and some have spikes so that other animals can't steal their water.
Then it wouldn't be a desert any more. Trees, plants and animals would move in and live there.
Well a lot of plants would die out because they aren't able to survive at those temperatures, but there would be plants that were able to survive, and probably others that would adapt to live there. There are plants that live in the desert which have temperatures higher than 45 Celsius, Death Valley can reach over 55 Celsius and there is plant life there.
An ecosystem is a place where plants and animals ( maybe humans ) live and animals and plants live in the desert so … 
The most common would be the locusts and grasshoppers.
Some of the plants that live in the Simpson Desert: Canegrass Acacia Parrot Bush Spinifex Grass
A person can live indefinitely in the desert as long as they have sufficient water and nutritious food and, depending upon the particular desert, shelter.
Succulents are plants that are able to store water in their leaves or stems which is a good adaptation to have for plants that live in an arid environment. No all desert plants are succulents, however.
Armadillo lizard, Desert tortoise, camel, desert rat are the only animals that live in the desert.cactus, Soaptree Yucca, Mojave Aster are the only plants to live in the desert
Xerophytic plants live in the desert scrub.