Usually, no—and you generally won’t need it.

On the EOS 2000D, red-eye reduction is not the same as the normal E-TTL metering preflash. The TTL preflash happens too quickly to make the subject’s pupils contract enough to reduce red-eye. Red-eye reduction needs a brighter light and a little time before the exposure.

Also, with an external hot-shoe flash, red-eye is much less likely in the first place because the flash tube is farther above the lens. Red-eye mainly happens when the flash is very close to the lens axis, as with many built-in flashes. Raising the flash changes the reflection angle from the subject’s retina so the lens usually doesn’t see that red reflection.

If the flash is used off-camera, red-eye becomes even less likely.

So the practical answer is: don’t expect the E-TTL preflash itself to provide red-eye reduction, but an external flash usually reduces the need for red-eye reduction anyway.