I guess you are asking whether the Java (Java Runtime Environment) is required to render the Telerik controls properly in the browser. I understand the significance of the question since when we access certain websites, a popup will be displayed to allow access permissions or telling the user that the website requires Java to work properly if either Java/JRE is missing. Java or Java Runtime Environment is required especially when the browser wants to run an applet (a small java code snippet which can be run in a java compatible web browser). In the case of Telerik RadControls, its entirely different and hence Java is not at all required to render the controls properly.
For best performance Telerik recommends the following things:
JavaScript must be enabled on all browsers
Caching on Internet Explorer must be activated
Browser scripting on Internet Explorer must be enabled