Would a wireless headset like this be compatible with a wireless router?

[modelamac]

I think the wireless headset communicates with the computer, not the router. The router deals with the ethernet function, not sound. Sound is part of the ethernet signal, which is combined or separated in the Mac.

Wireless headphones use bluetooth or an equivalent. She needs to find out the requirements (read the package/instructions) and see if her Mac will handle it. I don't know if all MacBooks do bluetooth.