No, Carbon does not work with Gecko, as the wiki indicates.
I had no interest in Qt when I ported Gecko so I didn't even try to support it and it doesn't appear as though the current maintainer, José, has any interest in Qt either. However, you're certainly welcome to try to add support for Qt. Take a look at GeckoBrowser.pas in the GetNativeWindow method - in only takes a few lines of code to add support, provided you can supply what Gecko expects.
That is, Gecko wants a handle to a native window. I'm not sure what that means in the context of Qt, which is already a wrapper around an underlying native GUI that differs by platform.
Of course, Qt includes WebKit, which might be a better choice than Gecko considering how big WebKit is becoming these days, with 90% of mobile device browsing being done with a WebKit-based browser (on iPad, iPhone, Android, Blackberry). Of course, you'd first have to wrap WebKit in an LCL control... In Xcode, you just drop a Web View onto your window.
Thanks.
-Phil