No and Yes, depending on if you live in the US or in Canada. In the US Radon Fans Don't Belong in the Basement. Most improper systems have the Radon fan in the basement or some other livable space in the house. This is a huge problem, and totally against EPA standards. It's easier to install a system like this, and it will get rid of the Radon in the basement.
In Canada, however properly installed fans and pipes will not leak radon into the building and are usually installed in the basement. When the fan and pipe are placed inside the home and combined with a ground level discharge, almost the entire system is located indoors, which helps to avoid problems that can arise from cold climates.