As POE needs usually some negotiator logic to power the port, and then generates 48 Volts, AND those 48 Volts will have to be converted somehow to the battery voltage the candles are using- surely it can be done, but in this case the "way will be the goal"- buying rechargeable batteries (and maybe make them fit in a housing under the candle in case they use those CR2032 Lithium cells) will be simpler in the long run and probably yield a better WAF (Wife acceptancy factor)
There are even rechargeable Button-cell batteries, like the Varta Coinpower series, if you really want to dive deep in such applications...