Welcome to open source!
Short answer: Yes.
Long Answer:
There are a lot of open source blog engines and "community" solutions out there. Having been in your shoes I can tell you that I chose Wordpress and haven't regretted it these past 18 months.
Regardless of which blog engine you decide to use you will want to get an idea of what open source is and is not. I can tell from your question that you have never read through the GPL which outlines the licensing terms you can and cannot use Wordpress (and other GPL software) under.
GPL is General Public Licence, it comes with WP and is also available at
http://www.gnu.org/
Specifically,
http://www.gnu.org/copyleft/gpl.html
A good FAQ on the subject (start here)
http://www.gnu.org/licenses/gpl-faq.html
You will want to know what GPL is in detail as Wordpress and other engines (as well as other software and entire operating systems) are released under the GPL.