Of course it's possible, although it's not the preferred way. There are discussions about security and so on and the appreciated way is to run web applications in /opt.
The easiest way is to use a contrib to install the wiki. MediaWiki is available as a contrib.
Have a look at this page, you may find another wiki application there.
http://wiki.contribs.org/Category:ContribNevertheless it's possible to run a web application in an ibay. You can simply install it there like you would do on another webserver.
Regards,
Niklas