The SharePoint 2013 Apps are divided into several types, depending on where they are hosted. The following list contains information about each type and whether Telerik UI for ASP.NET AJAX support it:
Provider-hosted (supported) - Developer or IT department provides the hosting structure for the application, so there is no limitation for the technology that can be used, including Telerik UI for ASP.NET AJAX.
Autohosted (supported) - The application is hosted in Windows Azure. In general Telerik UI for ASP.NET AJAX support Azure.
More information on SharePoint app model can be found in this MSDN article.