I have Premiere Elements 11 installed on Windows XP Professional SP3 32 bit, and it installs and runs well depending on the size/nature of project and pushing the limits of the existing computer resources.
When Premiere Elements 11 is on Windows XP 32 bit, it will be a 32 bit application with all the limitations of a 32 bit system, including maximum installed RAM = 4.0 GB of which typically 3.0 GB or less of that are available. Free hard drive space on the computer is another consideration. Single or Dual core processor enter into the equation and a lot of other factors.
But, yes, in accord the System Requirements/Minimum Requirements of that version, you can install Premiere Elements 11 on Windows XP 32 bit.