Hardly! If you put an object in empty space, without any other objects nearby, it will be completely unaffected by gravity. Unless the object is large enough that its own gravity can overcome its structural or material resistance to being crushed. Further, unless an object is actually in contact with another object, it is unaffected by gravity from its own reference frame. The apple falling out of the tree (neglecting air resistance) has no way of knowing that it is falling.

Well, unless that object was a single particle, it would still be affected by gravity. It would be slightly larger without the force of gravity attracting the atoms together.