They do indeed although in all my years of watching birds I have never been able to say I have definitely heard one.They do have a distinctive call as they fly, a very loud kind of cackling sound. Plus their flight is undulating.
https://images.app.goo.gl/QFFvTz619nU4XmWM7
As I indicated, my expert friend could tell but he is an expert.
Re' my reply to Mo.... I was generalising as most people 'hear' a woodpecker by its pecking.
I hope I haven't come across as an arrogant 'twitcher'.