We can set 'NavigateUrl' to value 'javascript:void(0)' to avoid the postback as below :-
<asp:treenode text="Item 1.1" navigateurl="javascript:void(0)" xmlns:asp="#unknown"></asp:treenode>
But not sure if you are handling its click to pass the value for the variable to page, which also might be affected. In this case you can use to set value to hidden field and can use it.
Hope this will be of help to proceed further.
Please let me know if any further help you need on this.