Can a gyro-copter soar? If one centers the gyro-copter in a thermal and then simulates a hover facing headwind; can the gyro-copter climb up like that ? 
Is it technically possible or is it advisable....
Any aircraft, from a helicopter to a 747, can soar. 

All it has to do is enter and maintain its position in rising air. How the pilot accomplishes that would be based on picking a strategy for staying in the rising air, and using his skill to do it.