Now my question is: does a Mega (or Nano/Uno) have the "horsepower" to drive that many WS2812B, while having a little bit of "loose" to read the card and handle the data ?
A Mega might work but an ATmega328 based Arduino (Nano/UNO) simply doesn't have enough RAM to store the color values. Also keep in mind that to access the SD card you need a buffer of 512 bytes that you cannot use for other tasks.