Hi,
I've not heard about using TestComplete with SB/XA applications before. TestComplete can work with any Windows application. So, I think, you can record and play back tests on the Rich Client UI. TestComplete may recognize the application's controls and provide special support for them or not. Also, it may access internal methods and properties of your application or not. The best solution to know is to try.
Install the TestComplete trial version and try recording and playing back a simple test on your application (just two-three clicks and keystrokes, e.g. filling in the login form). Use the instructions in TestComplete's Interactive Help or the Getting Started Tutorial for assistance.
If TestComplete can recognize your application's controls (if the client app is a .NET app), your tests will contain specific commands for simulating user actions. For instance, a click on a button control will be recorded as a call to the ClickButton method. If TestComplete fails to recognize controls, the recorded Click commands will contain coordinates of the click, for example, Click(12, 7). You will be able to record and run your tests in this case, but the tests will depend on the controls' position on screen, and if the position changes, you will have to update coordinates in test commands.
To determine whether TestComplete can access the application's internals, launch your application and then, in TestComplete, switch to the Object Browser panel. Here, you will see how deep TestComplete can see into your application. For .NET applications, TestComplete recognizes the applications' internal objects and has access to their methods and properties (see the attached image). This lets you call these methods and properties in your tests to perform the needed actions or to get the information on the application's state.