Different gyms do have different philosophies about competing at lower compulsory levels. DD's team had a preteam that taught them skills all the way up to what's now L4, but they didn't start competing until at L4. It's hard to remember back that far, but I think preteam did not have regular summer practices but encouraged the girls to do several weeks of camp AT THE GYM -- not at International Gymnastics Camp or Woodward, but at the gym for which they were eventually going to compete.
I think you should see what happens with the evaluation and if she makes the team, figure out what that means about when she's expected to be ready to compete and when the first meets will take place. If your gym does not do early season states in NY (and not every gym does!), it could be completely reasonable to train for six weeks out of the summer, heighten the intensity in the fall, and then do the first meet around Thanksgiving or afterward. To get a sense of the success of the gym's training program, look at where the higher level girls are, especially those who started out in that gym.