There are two forces operating on the block. A downward force due to acceleration and an upward force due to the rope.
Whether gravity is operating depends on where this takes place. If it's on Earth the answer is "yes - the Earth's gravity". However, it is on an accelerating space craft then acceleration is due to change in velocity rather than gravity. For the sake of simplicity, assume the experiment takes place on Earth, but it's worth mentioning that with the information given here you can't say for sure whether it is gravity or change in velocity that is causing the downward force.
