No it is not. The playlist is just there full time just so they don't have to spend the time putting it up and taking it back down every month.
When you play, your experience will reset at the beginning of every month (meaning if you're a 7 on 7th Playlist General, you'll get reset the following month back to private). Since your experience resets, if you have above 7 experience in every other playlist, every month you get a new chance to get the achievement.
Yes, it still has to be on the 7th. Bungie just gave themselves a lazy option is all.
:P