The device in question is just a micro-SD card adapter (converts it into a regular SD card), and has nothing to do with mobile SIM cards at all.
However, two types of devices do exist that can read mobile SIM cards. A simple SIM card reader (plugs in to an USB port) allows special software to read raw data from the SIM card, such as IMSI or contacts. However this device has no mobile radio and cannot communicate with any mobile network - you can't get internet, calls or SMS.
The other type of devices are mobile broadband modems (usually plugs into USB, sometimes PC-Card slots or other ports). They accept a SIM card just like your mobile phone does, so that they can connect to the mobile network and provide your computer with an internet data connection. With the bundled software, you may also be able to take calls, send or receive SMS, or edit contacts on the SIM card.