I think it is possible for a true believer to truly believe the Holy Spirit leads him into the political arena. I truly do not believe the Holy Spirit will do so.
I'll accept the burden of producing biblical reasons for my belief. I'll also accept the fact that these reasons may not be persuasive to anyone in particular.
A. The only government Jesus preached was His kingdom and the kingdom He would bring to Earth in the final eschaton.
B. Jesus explicitly de-linked His kingdom from the orders of this world.
C. Only in vanquishing and eliminating the power of the kingdoms of this world and in fully displacing the entire order of this world does Scripture tell us that "the kingdoms of this world have now become the kingdom of our God and His Christ" (Rev. 11:15), and that His entry into that exclusive reign is "destroying those who destroyed the earth" (v. 18). The inescapable implication is that everything about the order of this present age is destruction of the creation. When read with Romans 8:20 and Paul's reasoning there, it is clear that the powers of this age are part of the destructive futility to which all creation is subjected and from which our redemption awaits. Our redemption from futility is impossible to find in that very same destructive futility (which civil government/politics embodies). The suggestion that we can somehow "redeem" society or government or anything of it by our involvement is facially absurd (not instinctively so, but logically absurd and self-defeating).
D. When tempted by Satan, Jesus was offered earthly power. He rejected it. In keeping with this refusal of the Christ to embrace the powers of this age -- explicitly rejecting earthly power on more than one occasion -- Jesus set a model for His followers. Lest anyone say, "Well, He only did that because it was offered to Him by Satan," remember that Jesus was confronted by Pilate about His lack of earthly power as a supposed king, to which Jesus replied that He could (had He wanted) summon an army of angels to come to His aid. Jesus not only refused earthly power (and modeled that refusal for His church), but He refused even legitimate power that was rightly His in order to submit Himself to the Father. Revelation 12 says of faithful followers of Jesus that "they loved not their lives even unto death" and that by their deaths (through all ages) and their rejection and refusal to bow to the powers of this age, Christians overcome it by the word of their testimony and the fact that Jesus had shed His blood and had not loved His life unto death.
So the picture of Scripture in this final point is that all power which we might avail ourselves of is illegitimate except the power to die that He may be glorified. What will kill us? The very powers that Jesus rejected time and again, the very powers that will put His people to death (and already do), and that we are clamoring over to get a seat at the table. So, no, I don't see how the Holy Spirit will lead anyone to that.
Now, does that prove to anyone here or anywhere that Christians should shun politics and voting and political office? I seriously doubt it. But, the authority of the Bible is clear. The witness of Scripture is sufficient and without need of supplement by philosophy. What we get in the last 300 years or so is a heavy dose of philosophy by men that, let's assume, meant well enough. There is a way that seems right to a man but the end thereof is death. Moreover, I don't bear the responsibility of persuasion. Everyone must be convinced in his own heart of these things, and let us walk in as much peace with one another as we can.