No, it implements its own functionality. As an example consider one of the most basic controls which is available pretty much everywhere (i.e. no need for polyfill), the push button: the source code[0] for QPushButton clearly implements the behavior itself, it does not rely on any native button.
Compare with wxWidgets' equivalent to QPushButton, wxButton, where there is a backend-specific header[1] and implementation[2] where 99% of the wxButton functionality is there (there is a `btncmn.cpp` under `common` that is shared across backends but that has very little code itself).
[0] https://github.com/qt/qtbase/blob/dev/src/widgets/widgets/qp...
[1] https://github.com/wxWidgets/wxWidgets/blob/master/include/w...
[2] https://github.com/wxWidgets/wxWidgets/blob/master/src/msw/b...
I don't even need to dig through the paint loop. I've written QT software, and you can do it yourself.
Add a QButton with no styling, you will have a standard button widget in macOS and Windows (or a KDE styled one in Linux). Now have an event that modifies the button in some way (adding a CSS style to it is common, but also changing the sizing manually will usually do it) and the style of the button will immediately change to a QT-style one. The difference is so obvious in Windows and macOS, that it would be laughable to claim otherwise; but you can also just ask the QT Group devs or the community, they've reiterated/experienced this behavior plenty of times.