Yes, I'm using a 2600mAh phone battery to power my project.
I'm not running a real arduino as it waists a huge amount of power, and so I run an atmega chip (3€) and followed this instructions to have a minimal arduino that runs at 8MHz with the internal clock: Arduino To BreadBoard
I have the arduino (or atmega) sleeping for aprox. 1 hour and then, I power the GSM module and sensors. I read my sensors (Temperature, Humidity, Light, Distance) and I check the arduino battery and send an sms with the info and then it goes back to sleep again for 1 hour.
On sleep it runs under 50uA and when awake it runs under 200mA. When I started I calculated close to 2 weeks of run time and close to 1 month if I wait only 20 seconds for the GSM to register on the network but it would occasionally fail.
I power the arduino and the GSM directly from the battery and the voltage ranges from 4.2V (full charged) to 2.75v (full discharged). But I never reached 2.75v as I always replace the battery on the weekend.
All sensors are powered from the same battery through a 5v boost converter (some tiny device that raises the battery voltage to around 5V) but this runs for less than 1 second.
The GSM module (12€) I'm running is this:
Anyway, to be on the safe side and to run this for 1 month, if it was up to me I would just test the project with 1 battery, and then I would parallel 2 or 3 more batteries as needed. They cost less than 4€. Maybe upgrading to 18650 batteries would be a good idea, but watch out for fakes!
All my components were the cheapest I could find on eBay. An exception on 18650 batteries as there are a lot of fakes. Real and good ones are 2600mAh (max) and cost around 5€ (min).