Can I leave AVcc disconnected?
No. You must connect AVcc even if you're not using the ADC.  According to the datasheet:


  AVCC is the supply voltage pin for the A/D Converter, Port C (3:0), and ADC (7:6). It should be externally connected to VCC, even if the ADC is not used. If the ADC is used, it should be connected to VCC through a low-pass filter. Note that Port C (5:4) use digital supply voltage, VCC.