"Does their consciousness youth in time as well?"

According to General Relativity two things would happen for a group traveling faster than light.

1. To one another - other crew members and passengers on board - they would be the same age as the others on-board.

2. When they returned to Earth they would be younger to older others or the others left behind may be dead.

And General Relatively says that the speed of light is a constant. Nothing can go faster than the speed of light. So there's that.