I believe what you are talking about is called rec-ball.
I don't think there are any teams around who have practices and don't compete. Or any d6 teams for that matter since gfoa doesn't have a division that low. However there are a vast number of d5 teams out there who may let you practice and run drills with them. Just head over to your closest field, there's usually at least one d5 team that plays at every field in georgia.