If the conversion were instantaneous and not 'sloppy' in terms of explosions, mass ejections etc, the Earth would follow in exactly its same orbit without loosing a step. The planet Mercury, however, which is slightly influenced by a weak non-spherical 'tidal' effect due to the fact the sun is rotating and not a perfect sphere, would have a sight change to its orbit in terms of the precession of its perihelion.
A black hole of exactly the same mass as the Sun, will produce exactly the same gravitational field as the Sun at the same distance the Earth is from the Sun.