How does Powerline cope with line fluctuations
First, because communications-over-power schemes run the communications at some frequency well separated from the power line frequency.  Dimming the lights for a second is an event that happens in the frequency range of roughly 0 to 120Hz -- your Ethernet-over-power will be running at 100kHz to 100MHz, depending on the scheme.
Second, because it's Ethernet, so when (not if) the equipment on the power line inject some noise in there that interferes with a packet, the network will retry.