My initial response to this when I heard it years ago was to scoff. It seemed to me like another cudgel for politically conservative Mormons to beat me over the head with when I voted Democrat. But while it could certainly be (in my opinion mis-)used in that way, I don't think that's enough to dismiss it out of hand. Lots of true things can be misused; that doesn't mean they're not true or shouldn't be taught. And in the end, I think I do agree with McConkie on this point.
As a threshold matter, would Jesus even have voted if he had lived in a modern democracy during his earthly ministry? I'm not certain he would have, given that he wasn't too keen on getting involved in politics in his day.  But while I think he probably wouldn't have told people who to vote for, largely because he wants us to wrestle with those questions ourselves, I do think he probably would have taken part in a secret ballot voting process, both to be an example to others of doing one's civic duty as well as to substantively effect positive change.
And if you're going to entertain the notion that Jesus would have voted in elections if he lived in a democracy today, it's utterly fascinating (to me at least) to think about how he would have voted. How would he balance the good and bad policies each candidate espoused? Would he always vote for the one whose positions were the closest to the platonic ideal of correct, regardless of their chances of actually being elected? Or would he cast the vote most likely to do the most good? Heck, assuming his perfect (or sufficiently perfect) foreknowledge of events, it seems sometimes he would vote for someone whose stated positions and opinions he disagreed with just because some particular big crisis would occur that that candidate would be able to resolve that her opponent wouldn't!
In short, though, I think Jesus would enter the ballot box and mark an X next to a particular name. And while (again) I don't think he would tell everyone who to vote for or against , preferring to let his followers grow and debate and learn on their own, at the end of the day I'd like my vote to align with his if I could.
So yes, I want to vote how Jesus would vote. In practice, of course, we're all so so so far from Jesus in pretty much every conceivable way that an intense amount of humility is necessary here--we shouldn't just go around condemning everyone who votes differently than we do for failing to be valiant in their testimony of Jesus.  But I do think it's a good ideal to keep in mind and strive for, in our very imperfect individual ways.
What do you think? Is it helpful to have the idea of voting like Jesus would vote? Is it too liable to misuse in practice? Who would Jesus have voted for in your last municipal election? :)
 Be Valiant in the Fight of Faith, Bruce R. McConkie, October 1974 General Conference. And lest you think that this is one of those things Elder McConkie taught that the church just kind of ignored (**cough cough evolution being a deadly heresy cough cough**), it was quoted in a January 2017 Ensign article by Elder Christoffel Golden of the Seventy titled "Valiant in Our Testimony of the Savior" and is in the current Doctrine and Covenants/Church History Teacher's Manual for lesson 20 on "The Kingdoms of Glory."
 From what I understand, Jehovah's Witnesses take John 6:15 to mean that Jesus actively avoided all politics, and so should we. And at the least, Jesus seemed to avoid taking public stands on at least some contentious political questions (see Mark 12:17).
 With the exception, perhaps, of particularly bad candidates such as literal Nazis.
 At the same time, when we feel strongly (after due humble seeking) one way or the other, it's perfectly fine--and probably our duty--to encourage others to vote more morally, i.e., the way we believe Jesus would vote. This is hard to do without thinking that those who disagree with you are bad people, but (1) humility again, and (2) just because you see someone do something wrong doesn't mean you should treat them badly or throw them out. (I tweet-stormed some more thoughts on this spurred by a very interesting By Common Consent post titled "The Omni-Political Kingdom of God.")