No because the feather will be affected by resistance to the air. However, if feathers are bundled to weigh the same as the cup, they will fall at the same time. Weight depends on density, buoyancy and air resistance.
In a vacuum, free from resistance, both objects fall at same rate. Amazing. Ask Galileo, he got some things right
The concept of the constant acceleration for different objects due to gravity (at the same height and ignoring atmospheric effects) is usually attributed to Galileo. In reality, Galileo merely popularized the concept with his Tower of Pisa Thought Experiment (What happens if you drop a cannon ball and a musket ball from the top of the Tower of Pisa?).