Generally speaking, TestComplete can do automated testing for most any application. I'm not familiar with the specific application you're asking about but, if it's a recent .NET technology application, it shouldn't be a problem.
As for what scripting language to be used... it doesn't matter. The language to use for automation does not matter when it comes to creating automated tests.
You mention that some components are not being identified. This is possible, depending upon the component. If they are custom components then they may not have a direct match in what TestComplete can see. If you could post screenshots of the component in the application, what the Object Spy shows about the component (properties, methods, etc) or the Object Browser showing the component among others, that would be helpful in helping you figure out what's going on.
