There are lighting to USBC adaptors that work with the headphones, but not all. Some do data but do not do OTG data, which the wired headphone needs to work. So make sure you get a compatible one if you go this route.
In fact, you could try putting the adaptor inside an expansion card to have a lighting expansion card.
No, they will not. They say in the description that the adaptor does not support OTG. As I already told you in my previous message, you need an adaptor that supports OTG.
Let me explain in more detail. The adaptors you linked support data transfer, as in when you connect the iPhone to a computer, because the computer acts as the host. But these adaptors will not allow your iPhone to act as the host, for that to work you need OTG. Your usb wired ear buds need the iPhone to act as the host, therefore you need OTG, not only data sync.