So can it pass to be a complete sentence?
In the right context, it can be a complete sentence. Consider the fact that if you uttered just "Radharne," your user name on the Grammar Exchange, that would qualify as an abbreviated sentence if I had just asked you what your name was. In that context, "Radharne" would mean "[My name is] Radharne." Similarly, it is possible to imagine contexts in which "Next time, please!" would qualify as an abbreviated sentence. And what that sentence is would depend on the context.