"During system start-up, the voltage out of my power supply can rise to 27V (from a nominal of 24V). Will this damage the TPA3123D2?"
ANSWER: Though this is a less than less than ideal condition, the TPA3123D2 will probably not be damaged. It contains an over-voltage protection circuit that will shut it down when the power supply voltage becomes excessive. It would be advisable improve the start-up regulation of the power supply.