Sure...but you'd have to have as much as a planet weighs in order to generate one G of gravity from it. Now imagine trying to boost that mass into space...
Not completely. A denser than Earth substance would allow one to get closer to the gravitational center so that less mass would be required to obtain 1 g. As it happens if one could stand on the core of the Earth one would experience 1 g. (The massive core still being to much to launch.)