My practical experience is yes. It feels fully charged so far, but after a week, the box will be dead, which is more than I expected. I thought it would last longer, but it doesn't.
I did not consult Bose wireless headphones, and for the time being, I assumed that this product is just like this.
So if it doesn't work for a while, you have to charge it. The advantage is that with normal use, a full charge can be used for several days many times, so it feels OK.