No. The comedy wouldn't come through as it relies on manga timing. Not only that, but there is a chronology to the series, albeit a glacial-paced one, that heavily contributes to why it's so successful. It's not just a heehaw funny manga; it's also the joys and wonders of watching over a cute little girl's progression through life.
Turning it into an anime loses out on both of those things. Depending on run-time, the pacing would go to complete shit and many jokes would be stretched out and ruined. Alternatively, they would be hyper-condensed into 4koma-esque gag corners. Without infinite episodes to adopt everything, the sense of progression through life and the numerous callbacks would be neutered as the director would have to carve a particular segment of time out of the manga to adapt. Last but not least is that the mangaka's style changed dramatically over the years its run. Do they go with the Azumanga Daioh look of the beginning, or the more evolved and detailed current form?
I'm sure there's a lot more I can think up if I were to give it more than 3 minutes of thought, but perhaps the more pressing matter is why you make such shit threads.