K can catch or recover any kick behind the LOS and advance.
Where R comes into play is that if R touches the ball beyond the ENZ (and no non-psk foul occurs before the kick ends), which ever team is in possession at the end of the down will be awarded a new set of downs.
In your play situation, when K recovers the ball, the ball is still live. But K still needs to advance beyond the line to gain to be awarded a new series.
If R would have muffed the ball beyond the ENZ and then K recovered the ball behind the NZ, K can advance the ball and whereever they end up will be 1st and 10 for K.
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