Hello, I would like to know if it is necessary for all the VCC's and GND's of an Atmel Chip (ATMEGA328P-MU) to be connected for the chip to function properly? Thanks
Well: indeterminate. Unknown. Subject to change from chip to chip, or version to version, or depending on exactly what you meant by "function properly." "Yes" is the safe and easy answer.
I think you can get the non-analog stuff to work if you don't connect AVCC and the adjacent GND. Not sure how good an idea that is. Without knowing exactly what the internal chip design is, I would be cautious.
Also, each Vdd-Vss pair should be decoupled close to the chip.