I thought about it more... We have a giant rock - a small world in itself, but still just a pebble to the sun - dropping like an anvil into a ball of superheated gas. It has been falling through space for years and by the time it arrives it's moving like a super-bullet.
From the comet's perspective, each particle in its path arrives at its surface like a cosmic ray. So as it gets closer to the sun, it experiences a rain of particles, and the rain gets heavier and heavier. This "rain" will kick up a plasma on the surface of the comet, as the particles smash into the atoms of the comet's surface and splash them apart. As this surface plasma builds, increasingly the solar particles are colliding with the plasma and not directly with the comet surface. The cometary plasma is a shock wave travelling just in front of the comet as it approaches the surface of the sun. Some of the plasma will stream across the comet's face and out of its path, but the shock wave will grow as the density of arriving particles increases.
Eventually the comet and its shock wave will fall as far as the sun itself. If the comet is big and hard enough, I see no reason why it couldn't sink all the way to the core, where it might just drift around, melting and shrinking until it had boiled away completely, like an aspirin pill in a bathtub of boiling water. So I think the question is, what is the history of the shock wave of plasma that accompanies the comet as it falls into the sun? Does some zone form inside it, where the collisions are intense enough that fusion occurs, and if so, how large is it and how long does it last? Is it just a burst or is it a sustained burning that consumes a significant part of the comet's leading face? Or alternatively, does turbulence in the shock wave damp the force of its collision with the solar atmosphere, enough to mostly avoid fusion?
So now I believe it could happen. Though I would want to understand that shock wave, to really decide... Where did you get the estimate of "1000 times more than Sun's energy output in a second"?
It is important in my idea that it is a comet - that is large chunk of not connected ice, not a hard rock. As we know from examples of Tunguska event 1908 and Chelabinsk event this year, such bodieas tend to desintegrate on high altitude in large explosion because they quickly fall apart. Chelabinsk flash video. https://www.youtube.com/watch?v=OPSzpnHHwos
Estmation of the energy is based on the speed of imact, that is 600 000 meters per second (second cosmic speed on the Sun surface), mass of the object - that is 10++18 kg (based on water density and size...
Bolonkin & Friedlander (2013) argues that it might be possible for "a dying dictator" to blow up the Sun, and thus destroy all life on Earth:
Warning: the paper is published in an obscure journal by publisher #206 on Beall’s List of Predatory Publishers 2013, and I was unable to find confirmation of the authors' claimed credentials from any reputable sources with 5 minutes of Googling. It also has two spelling errors in the abstract. (It has no citations on Google scholar, but I wouldn't expect it to have any since it was only released in July 2013.)
I haven't read the paper, and I'd love to see someone fluent in astrophysics comment on its contents.
My guess is that this is not a risk at all or, as with proposed high-energy physics disasters, the risk is extremely low-probability but physically conceivable (though perhaps not by methods imagined by Bolonkin & Friedlander).