I am wondering if I can use that to put it to sleep/wake up during the light blinking process.
What about the timers and the USI?
Timer0 generates the interrupt which increments millis(), you might need that. Timer1 normally isn't needed (it's used for PWM generation if you do analogWrite()).
I suggest you program the fuses to use the 128kHz internal oscillator instead of the 8MHz one, and program the clock prescaler register to run the processor at the lowest clock frequency that you can manage with. This way, you can get the current consumption of the chip down to a fraction of a millamp while it is awake.If you do this, then I doubt that it's worth having the device sleep while blinking the IR LED, since the ATtiny current consumption will be tiny compared to the IR LED.