This really depends on the size, density and velocity the rogue planet was traveling before the collision and which planet it hit. As a side note, the possibility of this happening is quite rare.
If that rogue planet have sufficient velocity and under perfect conditions (such as the angle of collision), yes there is a possibility that it could reach the sun (bringing along with the 'planet' it collided say Pluto). The effect of that rogue planet would be enough to slightly disrupt other planets' orbit if it passes close and could disrupt the entire solar system. Pluto may not just fall to the sun based on the the pull of gravity, but also the velocity from the rouge planet.
Firstly addressing the 'sun' problem, yes if a sizable planet punches in to the sun, it'll create something like a mass coronal ejection which in return would bombard the solar system with harmful rays. Already this has affected the solar system.
If a sizable rouge planet hit one of the rocky planets such as Mars, large chunks of debris would come shooting out of the collision, a very high chance that a few pieces would land on Earth potentially creating another mass extinction; similarly to the other rocky planets such as Venus and Mercury. Similar to one of the solar system's gas giants if say, another gas giant hit it.
To summaries this, even a rogue planet entering our system would have already changed a few things not to mention a collision.
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