To resolve the doubt for people who ask it in the future. Taking advantage of the fact that I was being attended to in the VIP technical service (yes, as incredible as it may sound, it exists, but it doesn't differ much from the normal one. In fact, I entered the VIP branch because I hadn't received any new news about my case for almost a month. Well, this wasn't relevant, I'll continue) I asked the same question and, much to my regret, the answer was negative.
No, the protective case and the headphones are not compatible.