Hi,
I found that the module can (in fact it is right now in front of my eyes) work without battery.
All you have to do is power the module with a good 3.3V power source. I have an old ATX power supply giving more than 3A and it’s working OK. Use pin 6 for GND and pin 3 for +3V and also connect me module to your PC (this is very important).
Now you can enjoy your module without a battery, even with a SIM connected seems to be working OK (i.e. I’ve been able to send SMSs).
Regards,
Roberto.