Here is a great little demo that shows how to invoke Aspose.Words from an ASP.NET application AJAX style.
Aspose.Words for .NET by itself is just a .NET class library for document conversions, report generation and document programmatic access and as such does not have (and does not need) any built-in web or other fancy stuff. Therefore it is very easy to use from any .NET application be it an AJAX, ASP.NET, Windows Forms etc.