An Essix appliance is basically intended to provide a reasonably good looking temporary filler for the missing teeth, and to keep the natural teeth in place while the dental treatment continues. Eating with them is pretty risky, not to you but to the Essix device. You will also find that food gets under them a bit and you'll have to go and take it out anyway for cleaning.
So, if you have something you wouldn't have to chew anyway, like a soft summer fruit, go ahead! Anything else, you are probably better off slipping your custom temporary device out of your mouth.
Be careful never to wrap it up in a napkin - too many get thrown out that way - but to put it in the plastic case your dentist gave you.
Many people get Essix devices when they are having implants done to replace molars - if that's true for you, congratulations on your decision to take the very best care of your oral health you can!