I can say with some certainty that the NAS is incapable of distinguishing how a device is connected to the network. The NAS is, by design, connected to the network via a wired connection. The protocols used for communication exist at a higher level in the network chain than the physical connection. The network doesn't give an edge device, such as the NAS, any information about other devices on the network other than their IP address. The NAS has no way of knowing whether a device is on the wired or wireless segment of the network, that information isn't exchanged during normal communication.
Time Machine uses the Apple "bonjour" service for discovery. Bonjour relies on UDP communication over the network. It sounds like something is blocking UDP over wireless. Due to the nature of network communications that would have to be either a networking device (router or switch) or it would have to happen at the OS level.