Nope. That's how fields work: the black hole pulls on all mass no matter where it is. Just that its effect on earth will be less than that on the sun because of the sun's greater mass and in this specific scenario lesser distance to the origin of the gravitational “field” of the black hole. However, the fact that the sun gets a worse deal is no consolation if it means our atmosphere is suddenly ripped off, and the earth is given an additional acceleration towards the center of the sun. (because currently the earth's speed is just right to keep it in falling past the sun (i.e. in orbit), rather than falling into the sun, but this depends on the strength of the sun's own gravitational field and (to a far lesser extent) that of the other major bodies in our solar system such as Jupiter and Saturn.
The black hole would essentially upset the balance and if strong enough to rip the atmosphere from our earth it would certainly be strong enough to upset our orbit. Think of how the moon and sun affect tides, then remember that the moon is phase-locked with the earth because the earth's gravitational field essentially created a tide of rock heavy enough to stall the moon's rotation around its axis. Now imagine what a tidal waves in the earth's mantel & outer core could do.
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