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.