It could be it, though as noted, mine starts blooming at the end of June, and continues into fall, with the inflorescences aging to a cream colour and eventually to reddish brown.
There are other Persicaria species that are similar and later blooming, e.g. Persicaria polystachya, one I'm not familar with. Another possibility, perhaps (again one I'm not familiar with), might be Persicaria campanulata? A close-up of the flowers might be helpful, and also some idea of how tall this plant is. I've had mine for so long that I don't remember what it looked like as a young plant, height-wise or with respect to bloom time!
Edit: Okay, I see that you posted a flower close-up. It's definitely not Persicaria campanulata then.