The answer to whether one can trade Pokémon between an emulator and a DS is generally no, due primarily to technical limitations.

Emulators are software programs that imitate another system's hardware on a different device, such as running older console games like Pokémon on newer systems. However, emulating the exact wireless capabilities of original Nintendo 3DS (and even more so its predecessor, the Nintendo DS) remains challenging for several reasons:

1. Wireless connectivity: The DS and DSi models used proprietary wireless standards that were difficult to reverse-engineer accurately.

2. Server-side authentication: Many games including Pokémon required online access through Nintendo's servers to verify authenticity and activate certain features like trading between handhelds or with other players using different emulators could easily infringe upon these terms of service leading them being removed by developers themselves!

3. Technical limitations: Even if an emulator successfully replicated all necessary components needed for wireless communication there would still be issues related compatibility since each device has its own unique hardware configuration which makes it hard to achieve seamless integration across multiple platforms without significant software modifications.

For instance, DeSmuME - a popular DS Emulator that attempted this feat several years ago ended up facing legal consequences from Nintendo due to their unauthorized use of company servers thus they had no choice but disable the feature entirely within newer versions.

Trade pokemon 3ds emulator