I think only Tyranids could do such a strike and, in theory, not suffer the aftereffects of being horribly crippled since we've no idea of their total forces and the majority is in the black of space outside of Imperial reach.
Even so if you cut the head off the Imperium it doesn't mean the Imperium would fall instantly. First up if the Warp Navigation Beacon were shut down that would disrupt many other races using the Warp as well. So several armies might not even want to take out Terra for that very reason unless they use an entirely different form of transportation or they can replace it with something else. Heck it would be interesting if the Tryanids took it out and then the "moth to the flame" effect was proven to be valid and suddenly they lose interest in the Milky Way.
On the next point even if Terra fell you've still a highly military focused, highly religious faction that now has even more reason to focus on your faction above all others. The Imperium could fragment into various warring factions, but at the same time could have a united effort that reaches a fever pitch level of counter attacks. So you could win and then see your faction obliterated.
There's also a risk because the Imperium has lost a lot of tech and potential to its religious elements. Damage that status and you could see the Imperium suddenly abandon some elements. If the Imperium started doing hard science again they could see a technological jump for their armed forces that would be insane in the current setting of the Galaxy and would make the Tau advances look childish.
Heck maybe you cut the head off the Imperium and an even more dangerous one arises from the ashes that's even more Xenophobic, even more militant and even more religious to the Emperor and gaining vengeance.
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