I think the Iron family of languages is primarily for adding more flavours to the platform, allowing you to get into .NET using a language that you are familiar with. It lowers the bar a lot for getting new people with different backgrounds into .NET
Even though the syntax is Python, the implementation is still built on top of the CLR and the end product will not differ a lot if you decide to go for an IronPython project instead of say C#.
I've had some experience with IronPython and find it nice to work with (it helps of course that I really like the language). IronPython is now considered a first class citizen by Microsoft, and that is also the impression you get when using it. One downside to using it though is that it isn't as widely adopted as the two main languages, causing some issues when it comes to collaboration and maintaining a code base over time.
I found it particularly useful when doing a .NET port of a search algorithm that was first implemented in Python.
Regarding adding scripting abilities to your app, that is probably not the original intention with IronPython, but it has been done. The Umbraco CMS has (or at least had) the ability to create widgets using Python as a dynamic scripting language within their platform. A pretty neat feature to have.
You should go ahead and try it out.. It's always good to have more tools in the belt :)