How much memory it uses depends a lot on the format and what library is being used to stream the audio in the first place. If he’s streaming it via an OpenAL thing then it’s all just mix buffers that are getting upconverted to stereo anyway.
Also, what platform are you on that a micro-optimization like that is worthwhile? And why does it matter if there’s more memory available or not? On pretty much every gaming platform, either you’re using all the memory you can, or you’re not. If he needs to make more room for other things that’s one thing, but there are probably other places he can do that.
Ask him to actually measure the memory usage either way, and also, while most people might not be able to consciously tell the difference between mono and stereo, there’s a HUGE subconscious difference. Plus, by not having every piece of audio information competing for the center, you can get more dynamic range and texture, which makes it more pleasant to listen to.