I have two SharePoint servers one has session state enable and the other doesn't. There is a page in both  which uses filters with the JS API for create, set and refresh the webparts. The SP server with the session state enabled works like a charm but the other one has some weird behavior, lets say that the filters passed are not in sync across all webparts and the chart designer shows messages like root element is missing and does not always stores the configuration set even if it was applied. 
Is it possible that not having Session Stare for storage configured in the second servers causes this kind of issues?

Yes it is quite possible, since when there is no Session State enabled the web part will emulate session state using Application State or Web Part storage, however we have tested all these modes and they worked without a problem.

To see the actual configuration in which your webparts are operating you can explore the current configuration by clicking on the View Web Parts Config button in the main toolbar. The configuration settings of the webparts are explained in the following topic:

Getting Started > The WebParts Config File

You can also consider enabling the log file (explained in the topic referenced above) to see whether the webparts are recording some errors.

Best Regards,
Nevron Support Team