I don't have any specific experience with computer players for multi-move
chess variants, but I think it is worth noting that while a computer will
not be able to see as many TURNS ahead, it should be able to see just as
many MOVES ahead as normal. Depending on how you measure quality of play,
one could argue that they should play single- and multi-move variants with
equal proficiency.
Perhaps we should ask: how well do HUMANS play multi-move variants?