If you're splitting a stereo out into mono in(s), yes. If you only have one in, then you're losing one side of the stereo out, just be aware of that.
That is definitely a stereo to dual mono cable. No idea if it's appropriate for your application since you didn't say what that was.
Mixer out (two 1/4 L and R) into Boss Micro (mp3 recorder). The Micro has 1/8 input so I have a 1/4 to 1/8 stereo adapter on the end that fits.

So mixer stereo out, cable send and receive L and R into stereo 1/8 line input (with stereo adapter on the stereo jack 1/4 end).