No, running any kind of Arduino off AA batteries is generally a bad idea unless you
can take some kind of drastic power reduction type strategies such as sleeping the Micro,
or you are happy to frequently replace the batteries.
This reduces the power consumption whilst the Micro sleeps, but it also cant do anything
whilst it sleeps, apart from wakeup on specific conditions.
But this doesnt help if you are using a GSM module which draws power all the time.
Basically, you need to figure out how often the GSM module will be transmitting, as thats
the big power consumer, and that will determine the battery life.