In the absence of any direct rules stating whether R2D2's second vote is valid or not, I assume it will be up to the administrator of the voting booth (kyc) to make that determination.
You are correct - at least initially. And then there will probably be a lawsuit, regardless of which way kyc rules. Since we have no Associate Justice for Lincoln, I assume the whole Atlasian Supreme Court will have to hear it on first instance (as they probably ultimately would, anyway).
Hopefully, someone wins regardless of the questionably cast vote, and it won't come to that.