other than not eating (or drinking) anything 12 hours or so before your surgery (your doctor will give you explicit instructions) i know of no specific contraindications for eating celery when you have carotid artery problems. unless your surgeon specifically tells you not to eat it for some reason (i don't know your medical history) i think you can crunch away.
i eat a lot of celery daily. i'm about to have surgery on my caroid artery. should i stop eating celery if so when?