Yes you are more then welcome to use your hosted website with us to run 3rd party software such as PHPBB,Joomla and more. We offer an auto installer feature that will install and set up some of the most popular software for you!!
If you are unsure about a certain program or do not know if it will work with our servers please do not hesitate to post in our forum here: viewforum.php?f=45
(this is where we discuss software questions about websites).