Yes...exactly right. And, he was FEARLESS in battle. He demonstrated this a number of times: on the Monogahela, at Trenton, Princeton, Manhattan, &etc. At the ill-fated Battle of Manhattan, he had to be physically led away from the charging Hessians (the incident took place around present-day 42nd St and Lexington Ave.--there was an apple orchard there at the time).
We homeschool, and this is covered in the 4th grade curriculum. I frankly admit my shame at discovering just how much I had forgotten about this important part of our history.
We're transitioning to the American Revolution now, and I find I'm re-learning some of that, too.