Will this sketch eventually fail because of integer limit issue?
No, the sketches will not fail or work incorrectly. The Arduino "delay()" function calls the "micros()" function for timing. The "micros()" function uses the Atmel's TIMER0 clock and waits for 1000 microseconds (1 milliseconds) each iteration. The TIMER0 overflows about every 70 minutes, but the program code used in the "delay()" function handles that overflow correctly.