Do you mean powered of the 5volt pin of the Mega.
If so, that's a big NO if power comes from the Mega.
16 Neopixels could draw 16*0.06A = ~1Amp, plus the ~160mA of an ethernet shield, plus the 70mA of a Mega. That's way too much, so at least the LEDs must be powered externally.
I don't understand why you asked this question.
As said, the resistors must have a solid power/ground connection to the Mega, so everything is already powered externally.
Leo..