In a word...Yes. Just my opinion, of course. But I can't think of a memoir I've read, and I've read many, that didn't have an arc. I've been told that my own memoir, reads like a novel. I take that as a compliment.
I do presentations on life story writing. The participants do not intend to publish their memoirs. They are writing them for their family, usually. Even so, I always emphasize that each story should have an arc. A beginning, middle (problem presented), and end (resolution) is important in any kind of writing. If you want people to read your work, even if it's your kids, there has to be something that pulls them through the story, and that is the substance of an arc. ~Karen