4.5 volts voltage with the 74HC logic family?
The information you want can be found in the datasheet.

I take Texas Instrument's SN74HC74 as an example.

The IC cannot be damaged (lifespan is not affected) if you do not violate the Absolute maximum ratings.

See table 6.1 There it states that the supply voltage range is -0.5 to 7 V.
The - 0.5 V volt should give you a hint: this is the maximum rating, it says nothing about the chip working or not. Obviously at a supply voltage of  -0.5 V the chip is not going to work. But it will not be damaged either.

So a 4.5 V or lower battery voltage will not damage the chip.

In table 6.3 we find the operating conditions. Now we learn that the supply voltage should be between 2 V and 6 V for proper operation.

Below 2 V there are no longer any guarantees. Your chip might work even at 1.5 V. But all should work at 2 V.