Receive SMS from GSM module in a battery powered system
I dont think there's any command or built-in method to get the number of unread SMS like you want. The RING pin can be used as an indicator of incoming SMS or calls. You could set up an external interrupt to wake the MCU on the falling edge of the RING pin. The pin stays low for 120ms before returning HIGH. Then you can read the SMS with AT+CMGR=1. 

As a bonus, you can put the module itself in sleep mode by sending AT+CSCLK=1 and then raising the DTR line HIGH. This should reduce current consumption significantly. When an SMS comes in, it wakes up automatically and the RING pin sends a pulse that can be used to wake the MCU as explained earlier. You can also wake the module yourself by pulling DTR LOW. Read the hardware design manual for more details.