Can I power 100 ATMega328 in parallel?
I wouldn't string that many loads (boards) in series and expect good performance.  Mainly, I'd be concerned about noise and voltage drop.  

One alternative is to supply ~6V instead of 5V and on each board include a Low Dropout (LDO) regulator to obtain the 5V needed to run the board.  And if you have the room, you could use 24V as your main supply and install a small SMPS at each board to provide the 5V; this way you would be connecting and routing 1/5 the current as you would by supplying 5V.

Also, I would try to avoid passing the power supply through the foil but use vertical PCB mount bussbars to route current across the board.

Ten-amp connectors shouldn't be a problem unless you have extreme size restrictions.  Multiple pins can be paralleled to increase the ampacity.  Twenty amps might be more of a challenge.