You should be able to. If it has a permanent magnet rotor, it would produce current just by spinning it. But I don't think you would get the same amount of power out at the same speed simply because of the inefficiencies. A motor will always take more electric power than its actual output, and will always produce less electric power than what it takes in the form of mechanical energy.  
 In short, I don't think you will get 35kW at 18,000RPM.  
  

 To your second question, the answer is yes, the motor (or a generator) will produce more power at higher RPMs, but this will mean both higher voltage and current than what its windings (wire and insulation) and contacts were rated for.  
Overheating will not be the only problem, but also the stress on the insulation AND the mechanical stress on the whole structure because of significantly higher forces at higher speed. Additionally, hotter wires and frame would have reduced mechanical strength, and things might start falling/flying apart.