As it stands, no NDS emulator will have local downplay support nor WiFi support. For local download play, the Nintendo DS expects 0 latency due to the proximity of the DS consoles. So there must be 0 lag for it to work and the NDS has a very low tolerance for latency. Even if you have a very fast connection, the latency of simply having your request routed through your ISP and the servers until it eaches its target would cause download play to fail. People have tried in the past but they all failed to implement download play because of this.
Now only is latency is a problem but download play and WiFi uses RSA encryption to verify the data is from a Nintendo DS and hasn't been tampered with. As to this day, no one has been able to break the RSA encryption used by Nintendo so its impossible for a NDS to add in official WiFi support since the Nintendo DS requires a RSA encrypted connection to the Nintendo servrs before connecting to other people.
Now there has been projects to tunnel download play across te internet on the Nintendo DS itself (Though it would require third party hardware and modifying the NDS), but they all failed due to what I stated above. For download play to work you need 0 latency which no ISP is capable of maintaining.