Since we don't know what you are doing with the data from the GPRS it is hard to tell. If you are just printing it to the screen it should be fine. If you are doing any processing on the data it will happen at half the speed of the 5V part.
You couldn't just hook the LiPo up to the GPRS module. The work up to 3.6V is probably an ABSOLUTE MAXIMUM rating, not a recommended one. Connecting 3.7V is above that maximum.
But actually a 3.7V lipo has a fully charged voltage of 4.2V, so you would almost definitely destroy the module by connecting it to the battery.
Depending on what regulator is used on the mini, you could connect the battery up to it, and then use the 3.3V output of the mini to power the GPRS module.
Ignore me, I looked up the part and the datasheet says it operates over the range of 3.2V to 4.8V, so you would be fine conecting the LiPo directly to it. In fact according to the datasheet, it is DESIGNED for use with a 3.7V LiPo battery.
Thank for your answers!! @KeithRB: I am going to power the attached GPRS shield to send mainly data to a remote server. The data will be a string of about 30 caracaters. I have not defined the frequency of the transmition, but it can be between 10 sec to 1min.
@Tom: Where di you find the datasheet. From the seller web site there is nothing. They really do not provide a lot of information and the support is null. They only quickly reply me that the module works under 3.6V, But I also read something like you stated 3.2-4.2.
My project consist only of Arduino Mini Pro 3.3V, a small data logger the record the last GPS position (in case of the GPRS is not available), the SIM908 module and a battery loader module (to load the battery with USB). I am just worried about the Mini Pro frequency. I would like to make sure that the GPRS module support it for sending mainly data, but to get and send text message, and very occasoly, get phone call.
I also tried to use Arduino mini pro 5V with that SIM908 shield ( with a power regulator to power the GPRS module at 4V), but I have never been able to make it working. It seams to have a power issue, but the seller never provide me clear answer :o(