While you can harvest the whole celery plant, I would resist doing this. You can just snap or snip the outer celery stalks since the plant will keep producing more stalks.
Right before frost, I will cover the celery with a hoop tunnel and plastic. This will allow me to still harvest celery into early December depending on how cold it gets.
If you harvest the whole plant, you can store it in your refrigerator drawer for about 3 weeks. Since I am harvesting a few stalks at a time, I prefer to cut them as I need for stew or soup. Since I like to use the celery for salad or for a cold crunchy snack, I cut the celery stalks into thin strips and then store them in a container of water for about a week or a little more!
If you don’t know how to Sow and Grow Celery, just click on the link.