Yes, but you need to consider first what are the required power supply and other components for SIM800L module. (See the Datasheet)
SIM800L module's input power supply is 4.0V (3.4 ~ 4.4V) to make it work properly, also the serial logic communication of SIM800L is 3.3V output. Then we all know that Arduino/gizDuino is 5V powered and the serial pins output is 5V logic. Their serial communication is not compatible, so what we gonna do for that? You need a Voltage Translator. Which it can converts the voltage from HIGH toLOW or vice versa.
Multi-voltage level converter: http://www.e-gizmo.net/oc/index.php?route=product/product&path=59_66_103&product_id=16Tags: SIM800L module