If that's what you want to call it. I always thought of burnout as not being able or not having the desire to continue keeping up the professional pace that you've been keeping over a long period of time. It doesn't have to include any irrational element, or even explode into a cathartic moment to be burnout as far as I've heard it discussed.
'Succumbing to burnout' I get - 'having a burnout' is not a phrasing that I'm even familiar with.