Yes, it's possible especially on Joomla version prior to 3.x.
This mainly happens because of conflicts between multiple inclusions of the jQuery library also used by chat component.
Unfortunately until Joomla 3.x has been released, no standard way to include jQuery library was available for developers. As a results every developer using jQuery in their project included its own version of jQuery library.
This led to a real 'jQuery hell' where a lot of files related to different jQuery version was placed inside page HTML, with obvious malfunction. Starting with Joomla 3.x this problem is progressively decreasing.
Is not assured that also on Joomla 3.x some developers choose to not follow Joomla standards and include its own jQuery version. If you experiment such a problem, you can use controls offered by JChatSocial configuration to exclude jQuery inclusion or change compatibility mode for script loading.