Protecting a comparator's input from overvoltage during power up/down
You might be OK with no modification: -



My thinking is that you will never exceed +/- 5mA even when the device is unpowered - this current is usually the maximum current that the input protection diodes should be run at.

However, TI's data sheet gives no real clue here unlike data sheets from other suppliers so there is no real way of knowing.

For the input disconnection idea I'd be more inclined to clamp the input at 0V with a MOSFET until the 15 V rail had risen sufficiently.