3 stage/cascade voltage regulators
No - not without due precautions.

SOME regulators will withstand this.
 Many will not or may not.

Place a reverse polarity diode from output to input of each regulator so that if Vout > Vin the diode will conduct and charge the input capacitor or whatever. 

This problem can occur in real world applications.
 Largish output cap.
 Input short of bus to ground or fuse blows and some other load rapidly lowers Vin.
 Vin now low, Vout now high, Vout cap discharges into regulator and destroys it



From page 11 of NatSemi datasheet - here.
 Pay no attention to the man behind the curtain when he says a 1N4002 is a  fast diode. It's OK here. 1N400X.