The risk of damage depends on which circuit is touched and where it is in the circuit. Some, if grounded will do nothing more than shunt the signal to ground and make it disappear. Others, like at the speaker output terminals, will cause that circuit to pass infinite current (theoretically) and will kill that stage. In some amplifiers, it will take out even more than that. It's not a good idea to use any part of your body to touch the circuits directly. It can be relatively safe but under the right circumstances it can be lethal, like in a tube amp when you contact the plate circuitry which can carry well over 300VDC. At no time is it a good idea to touch any circuit with one hand and the chassis with any other part of your body, especially if it's on the other side of your body from that hand. Touching the live circuit with one hand and the chassis with the same arm can be bad if the voltage and current are high enough but the current isn't passing through your heart- it doesn't take much to stop a heart.