It appears Qt5.8.0 has the GTK3 style. The library libqgtk3.so is present in the plugins/platformthemes folder.

If an application is run with:

QT_DEBUG_PLUGINS=1

It appears this library is loaded successfully as the following is detailed in the output:

loaded library "/opt/Qt/5.8/gcc_64/plugins/platformthemes/libqgtk3.so"

However, the application does not use the GTK3 style.

With the following code implemented within the application:

QStringList keyList = QStyleFactory::keys();
foreach(QString eachKey, keyList)
{
    qDebug() << eachKey;
}

The output is:

"Windows"
"Fusion"

gtk3 is not listed as an available style.