No, it sounds perfectly fine. Mathematically, interleaving samples like this is equivalent to zero-padding every other sample to upsample, with no antialiasing filter. Then you add the other channel offset by one sample. The end result is that you have both channels summed up in the low 24kHz of spectrum, with half a 48kHz sample of offset for one channel (mostly negligible), and everything mirrored in the top 24kHz of spectrum as aliasing (which you can't hear). In other words, it will be very, very close to what a simple mono downmix would sound like.
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