I am looking for a low power solution for my ATmega32U4. It uses Serial1 to communicate with Bluetooth, so I need to have it active. When I receive data from Serial1, I want to power up the Arduino, do some magic, and then power it off...
For Power Down/Standby Mode you would have to use an Interrupt Pin to reactive the MCU. If you do not mind possible loss of the first character you could connect an Interrupt Pin to Serial1 RX and wake up on the first start bit.
The startup delay (i.e. time until UART is up and working) may impact the first character received. You could always start off by sending a number of null character as a "wake up call"; classical break sequence.
Ref. ATmega16/32U4, Chap. 7. Power Management and Sleep Modes.