No, you can't install Bluestacks on Windows XP Service Pack 2 because this version lacks features found only in Service Pack 3. The features are required for the application to work correctly in terms of Kernel procedures. It is known that if you try installing Bluestacks on XP SP2, you will face an error telling you that Bluestacks doesn't have support for this version of XP.
To make it work, you might need to install Service Pack 3 or upgrade directly to a more advanced version of Windows.