Bohm,
I would say that the question of whether there is no gravity or it being cancelled out is at the outer edges of my knowledge. The reason I would tend to go with it being cancelled is because I am looking at it from an engineering problem point of view. Since gravity acts as if from the point centre of the mass then at a delta distance away from that centre there would be some very small gravitational force. This is because as per the shell theorem that mass beyond the radius of your test dummy does not act upon it. In other words if your test dummy was halfway to the centre of the earth all of the earth's mass that sits above that radius has no net effect on it.
On that point I would agree with Viviane that it is merely that your acceleration is zero. It would seem to me to be a fairly meaningless distinction from a practical point of view however since it is a single point in space.