I'd have to say in general no, but what you really need to do is try recording and replaying on the application. In my case, the web add-in is sufficient. There is not really an 'AJAX' addin, but there is a web 2.0 toolkit that may be helpful.
When I first started using QTP against the current application, it supported all the objects within the application without issue. The big issue I did face was syncronization, as there was no real built in type that would work, and I ended up having to make a function to deal with it. Unfortunately the function in this case is app. specific, so it wouldn't really be any help to you. If you do search on AJAX and synchronization there are some decent resources that should give you ideas.
You may not even have any issues with syncronization. You just can't tell until you try.