When discussing the relative pronouns which or that, the rule indicates which is used to introduce nonrestrictive clauses and that is used to introduce restrictive clauses.

Whatever the rule, it is my opinion that both pronouns are overused. Take any writing sample and see how many times you could delete both pronouns and the implied and initial meaning remains unchanged. For example “I think he should post again” compared to “I think that he should post again.”

However, considering the phrase in question is referring to a specific call, I might suggest the following to be preferred: “your call will be answered in the order that it was received.”

I am not even sure your question of using ellipsis is the one that should be considered. You are using two coordinating conjunctions as an interrupter—are you trying to communicate concession between the event you witnessed, the need for action, and your lack of it, or…

Students who have prescriptive grammar instructors tend to ask questions like yours. It is only my suggestion, but consider asking if your syntax, punctuation, and diction are communicating what you intended, rather than focusing on what is deemed correct.