No , the center of gravity is in a spot where balance is achieved, if an object is dimensionally heavier on one side, then the center of gravity would not be in the measurable center.
Only if the object is homogeneous, i.e. the mass is uniformly distributed. If the object is lumpy, or has thick spots and thin spots, then the center of gravity isn't related to the geometric shape....
The center of gravity is the point at which your gravity attracts others, and others are attracted to you. This makes it your point of balance since balance is relative to the center of gravity of...