It doesn't matter if you know little about Japanese culture when you watch Azumanga. Funnily enough, Azumanga can often end up an education in the subject - I came away knowing alot more than I did when I started! If you get the R2 releases (I can't speak for the R1s) ADV has packaged little booklets with all of the Japanese "in" jokes completely described, so you'll be fine.
It's a hugely funny series, and I -was- going to say it's something I feel eveyone should watch, but noting the battering I got for saying that elsewhere, I refrained. (....watch it!)
Also, although I haven't heard all that many dubs, I'd say Azumanga is the best I have heard. All the characters are portrayed properly, unlike in some other dubs where the voice actors sound very removed from the whole situation. After listening to the English/American Osaka and Chiyo, it's very difficult to listen to the Japanese ones, in my opinion, which is rather impressive.