I was about to suggest something like this when I found this question.
In the absence of an option for "push notifications only", I suggest that there be an option to "synchronize only once/day if there are no incomplete shipments."
Goal here is to reduce battery usage when there are no known packages to track. I don't think there should be an automatic "no synchronize" as packages can be added automatically through your EBay or Amazon accounts. And in those cases, I think once check per day is sufficient!