I have known several people who only have the use of one hand, and two of them play kalimba. Kalimba Magic offers a special one-sided kalimba, either in a left handed or a right handed setup.
It seems you would need both the left and right hands to simulate the full kalimba experience. The theory is that the kalimba evolved from huge log xylophones, made from actual logs, which were played by at least two people, one on each side, playing interweaving parts. The kalimba plays those same two parts, but the two players who used to play on opposite sides of the xylophone, are both now sitting inside the player's head.
Yes, left and right hands playing interlocking parts is fundamental to the traditional, two-sided kalimba, but it is most definitely possible to play one handed kalimba and sound good. When you play the one-sided kalimba, you are playing something set up very differently from the two-sided type. The notes are laid out in a linear setup and are played using different rules.