Probably not ... I can imagine a delay command would result in the Atmel chip to cause some idle time. The Atmel chip might get warmer over time (slightly?even a delay does not prevent this) warmer when running full time code, however if it has a possibility to release its heat I don't see a problem. But mostly only overclocking can cause really serious problems, or using the Arduino in a fully closed box or in a hot environment.
In comparison: many computers are running for years without switching off, the Atmel (chip) is in that sense no difference, as long as generated heat can be relieved.
You can read more about a heat sensor in Atmels here: Internal Temperature Sensor