VCC's and Gnd's

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

http://www.atmel.com/Images/8161s.pdf

Yes.

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.