When adding a COSM or loop effect to an already recorded track, this effect does not actually get recorded onto the track. This is so that you can freely change the effect parameters or turn the effect on or off.
When exporting tracks as WAV or AIFF files onto a computer, the data that is actually recorded onto the tracks (i.e. the original, dry signal without any effect) is what is exported as WAV files. This is why there are no effects present on the WAV or AIFF files when exporting.
There are two approaches to recording effects onto tracks:
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Stereo Mix
You can bounce the tracks together into one stereo track (also known as a mixdown). This bounced stereo track will include all tracks as well as any effects.
Stamping an Effect Onto a Single Track
You can bounce the track, with its effect, onto an available, empty track.
After following one of the bouncing procedures above, you can export the bounced track(s) to a computer that will include effect(s). See the "Putting multiple tracks together (Bounce)" in the BR-600 Owner's Manual.