Exactly! Recall that the special effect of something being a black hole is felt only at the surface. As the Earth, and other planets, are nowhere close to the surface of the Sun, they will continue to feel the same gravitational effect as that of the Sun.
Of course, because the Sun is now a black hole, we won't be able to receive any light from it. Life, as we know it, will come to an end. But, apart from that, there won't be too much of a change.