Here is the link to the paper:
Design of Quantum Circuits to Play Chess in a Quantum Computer:
I missed this post earlier.
It's very interesting that there has been some progress on this - at least people seriously starting to have a go at it. If, as it seems, there are no fundamental barriers, the end of the road will be a quantum computer that solves chess, answering the OP question!
I am however inclined to observe that there are a lot more useful and important things to do with quantum computers!

#6937
All evidence indicates that it will be: white to play, black draws.