No you cant, all power used down the chain will have to be provided by each upper link.
What stops you to power them in parallel from one, sufficiently big source?
Cut into pieces of two. 2 wires (plus and minus) come in at one side, 2 x 2 wires come out at the other side. One pair to Arduino, other pair to next Arduino?
Of course you can use fancier connectors; maybe 9pin subD to carry power and signal.
I can't advice what voltage I would use for the power supply. If longest distance is relatively short, your power supply can be 5V and must deliver sufficient power to feed all nodes; thick wire will help to reduce loss.
For longer distances you're probably better of with 9V or 12V power supply and convert the voltage down at each Arduino. Others might be able to advice better.