Can Qt Creator recognize TODO and FIXME comments?

Yes, go to Help / About Plugins... menu, under the Utilities section you will find the Todo plugin, so you simply have to enable it. After restarting Qt Creator you will see the To-Do Entries button on the bottom of the main window, which opens up a panel listing all TODO, FIXME and so on comments.

The plugin has some minor issues, the one I remember is that international characters are not displayed correctly, but in general it works quite well.

There is a Todo plugin which enables this feature. It is included since version 2.5 (https://blog.qt.io/blog/2012/05/09/qt-creator-2-5-0-released/)