Sorry, but if I understand your question correctly, then NO.
The Korg 01w generates it's sound using one system, probably peculiar to Korg and Korg devices. The Yamaha will use it's own system. Both devices can receive instructions via midi, but each will generate sound based in the electronics in it's own box. Even though both boxes may have many sounds labelled the same.
The Yamaha may well be able to 'play' sounds on the Korg if you connect the midi OUT on the Yamaha to the midi IN on the Korg. Then, the Yamaha is generating a midi instruction, which is turned into actual sound on the Korg. In this case, do not use the audio output on the Yamaha, but use the audio output on the Korg.
If the Korg is a keyboard (I think it may well be, rather than a module/Tone Generator), then you can do the same in reverse, i.e. connect the midi OUT of the Korg to the midi IN on the Yamaha, in which case the Korg is generating midi instructions which are being turned into audio by the Yamaha.
It may be possible, by playing with the active channels on each device, to create a midi file that will play back using certain sounds on each device separately, i.e. use the 'best' sounds on each device.
So, by using the right connections of midi, AND audio, the answer to your original question could be 'YES - sort of'!!
Geoff