At this moment I started to browse support forum for this component. And realized that a lot of people were having trouble with the same plugin. Authors were answering questions but what was clear to developers was not clear to users. After some experiments based on forum discussion I realized that solution was really simple.
It is necessary to go into JCE configuration from JCE admin menu (under components section of top menu). And to add string script[*] into Extended Elements field. After saving this you can open HTML window (edit HTML code button) in JCE editor and enter your script into it. After updating and saving your page will contain inserted code.
As en example, if you will enter:
You will see something like this banner on your page:
Using JCE with this script plugin is not the only one method of inserting script code into your page. You can disable WYSIWYG editor, enter the code and then enable your default WYSIWYG editor. But I prefer to use described above method.