I'd absolutely love to hear the rationale for this type of training. Is there a time and a place for aerobic work in a predominantly anaerobic sport? As mentioned by someone within the thread - Yes. There are definitely some athletes that need this type of training regardless of sport, but not necessarily long-term. The adaptations can be made fairly quickly and actually last for quite a while.
On the flip side, if you take an athlete that doesn't need this type of training and you can actually cause changes to the physiological properties of certain muscle fibers (you can't change muscles fibers...you have what you have...can only change their properties to some degree) and actually make them slower/less powerful.
So, how do you know? There's a few ways, but probably the easiest is to monitor resting heart rate (HR). Most high level gymnasts will probably be in the 60-65 BPM range or below. That's a guess without actually looking it up in the literature so if you've seen a study to suggest it's slightly lower/higher...that's my disclaimer with the numbers I'm spitting out. Ultimately, I'm just trying to illustrate a concept. Anyway, if your athlete is up in the 70-80 BPM or higher, some aerobic work might be warranted until they get their bodies adapted back down into that lower resting HR range. But, once they get back down in that range, any conditioning should be geared more towards strength/power/anaerobic endurance-type of training. Remember, the aerobic system adaptations tend to last longer as opposed to the anaerobic adaptations. Note: You'll always lose a little, regardless. Unfortunately, these energy systems operate on a continuum and they "compete" with one another. So, if you shut down the aerobic work and go immediately to anaerobic work, you will lose a little of aerobic gains. But, those losses should not be too bad.
Feel free to pass this along to your coach! Good luck!