input amplifier higher than VCC
In short: probably not.



The datasheet of the component (if it is actually a decent one) will tell you when there is a high risk of damaging the component.

Those conditions are listed under "Absolute maximum ratings". Note that these values can be higher than the one listed for normal operation and you should not expect the component to work as expected outside the normal operation range. The only thing you can expect that there is no fatal damage to the component as long as you stay inside the absolute maximum ratings.

Typical values are temperature range, supply voltage range and input voltage range of the individual input pins (often with respect to the supply voltage). For outputs there is a current limitation (or a short circuit duration). And you find a total power consumption specification. And even more or less depending on the exact component.



What about an opamp output?

The opamp output stage is inherently limited to the supply voltage of the device. It cannot go beyond the positive or negative supply voltage even if the gain equation would require it to do so. How close it can get to the supply rails depends on the implementation of the device. Some swing to a few millivolts to the rails, others need a headroom of volts.

So by this alone you cannot damage the opamp output. What you should consider is the load to the output. Will the output current of your opamp stay below the limit imposed by the normal operation specifications? 

Second consideration then is the power consumption of the opamp. Even if the output current is in the specification the total power consumption (or temperature rise) might be exceeded if you are working at the limit of voltage and current.

(You typically don't want to stress the component to the absolute maximum ratings)