Well, the political and social effects of this doomsday scenario are dependent on how bad the extinction is.
Best-case scenario, Earth gets lucky, the subspace window opens in the upper atmosphere, relative velocity is minimal, much lower than an asteroid impact, and a shotgun spray of cometary ice messes up a continent.
That would throw a massive wrench in the UEF's plan to win the war, and it would do nothing but benefit the GTVA. Hell, the Tevs might even consider broadcasting "Our Gef allies dropped a giant comet boulder on your puny heads! Surrender, or we will send more!" After all, in this scenario, it wouldn't be any worse than several dozen nukes going off, and without any of the nasty side effects of radioactive fallout. You might have some mild crop failures, but the short term effect of losing population and infrastructure is going to be a lot worse than any debris the impact propels into the atmosphere.
The Tevs initially set out to hold Earth hostage with orbital bombardment. That's why command sent Bei & his multitude of beam cannons. It's pretty reasonable to assume that if the Vishnans had not interfered and dragged them into alternate-reality Shivanland, Bei & company would have followed through on the threat, and would have started vaporizing cities.
Aside from being much more random in its distribution of destruction, the comet strike would be mostly the same as a post-bombardment Earth. The Tevs are now in a great position to begin landing and annexing the planet (though it's stated somewhere that there are not enough marines in the whole GTVA to occupy even one continent on Earth).
Now let's consider the worst case scenario:
The cometary debris smashes into Earth at 60+ km/sec, possibly the highest-velocity impact Earth has ever seen. The blast vaporizes a continent and propels a measurable percentage of Earth's mass into various suborbital trajectories. The fireball boils off a decent fraction of the oceans, wrecking all the shallow ocean biospheres. The heat wave encircles the planet, igniting everything flammable. Plant life fails on a global scale, and the fires burn off the last of Earth's precious oxygen.
This planet is no longer worth fighting over. Everything the GTVA came here to do was a massive waste of time. On top of this, the dream of returning home to Earth that propels the Terran half of the GTVA is forever shattered.
Crushing debt alone will probably force the Terran half of the GTVA to implode. Maybe Khonsu II can save them all, maybe Khonsu II can deal with the inevitable Terran backlash & NTF-effect. Maybe the Vasudans just detach from the husk that used to be the GTVA, and go do their own thing for a while.
The Tevs can actually gain a lot from this if the physics (or lack thereof) cause the impact event to be not-that-bad. But as the damage inflicted by this event increases, it starts to get disadvantageous for the Tevs.
Of course, it could be even worse than that:
...This is (AFAIK) why BP tries not to examine the specifics of subspace in any in-depth way beyond how it applies to the strategic situation, because otherwise one wonders why SSMs don't just slam into targets at c-fractional velocities.
If subspace can
be used to induce c-fractional velocities...hoooooooooly crap. A measly 0.01 C, or 1% lightspeed, is almost THREE THOUSAND km/sec.
This is death-star-level destruction. There would not be an Earth after this.
...But as it concerns the Tevs & Buntus, an impact of that magnitude is no better or worse than the 60+ km/sec impact. Earth is equally useless & unusuable as either a sterile ball of rock, or a pulverized mess of vapor, dust, and asteroids.
PS, I do use subspace drive shenanigans to propel things to crazy-high velocities in my upcoming mod. The GTVA doesn't do it because of accuracy issues (can't hit the broad side of a sathanas) or strategic value (planets are worth more intact). The Shivans, on the other hand, used to do it all the time, until they invented more efficient and destructive strategic superweapons