Arduino Fio: Battery/Solar Powered Weather Station
You have a LiPo charger module. It's meant to charge single LiPo cells. It is therefore, the intended safe use that you can connect any single LiPo cell to it. All single cell LiPo batteries are nominally 3.7V. The only real question might be -- does the charging circuit try to charge too fast?

A 2000mAh pouch LiPo can safely be charged at 1X the capacity. So a maximum current of 2000mA for an hour in this case. The battery management chip has a maximum charge current of 500mA, so there's no way it can reach over 2000mAh of current while charging.

The datasheet for the battery management chip shows a R_PROG resistor that basically sets the maximum charge current.  Section 5.1.2 shows the formula for charge current regulation at:

I_REG [mA] = 1000 [V] / R_PROG [kΩ]

The schematic for the Fio shows they have used a 2k ohm resistor.

Thus: I_REG [mA] = 1000 [V] / 2 [kΩ] = 500 [mA] (the maximum the chip can operate)