Funny you should ask. This is my new team here at Microsoft.
To your question, yes anything you install through the WebPI will get updated through that tool. You don't need to go elsewhere for anything in there. The way this works is that the tool checks a manifast file and if there is something new or updated it indicates
this in the UI. You click it and BAM you're getting updated
EDIT: With regards to your question about WU, no, it wouldn't show up there.
EDIT 2: I'm doing a crummy job of answering your question Barry. Basically you have to run the tool every so often to see if there are updates. It doesn't "push" things to you like WU does. Hope that's more complete