Just look at Telegram as a real example and compare that against the other messenger apps since the majority of them use Electron and Telegram uses Qt for some of its desktop clients.
If those other apps are using Electron then yes; Telegram is smoother.
> In general, would you say that Qt is supposed to work just as buttery smooth and native on Mac or iPhone as a native app?
Yes. No difference in RAM, Disk, or CPU usage than any other native app.
> And will an OS built on Qt like Ubuntu Touch will be as smooth and beautifully craftable as iOS apps on iPhone?
Yes. One example is AsteriodOS which is an OS for smartwatches built using Qt. [0]
It's also not that performant compared to something like KakaoTalk (not sure what they use..perhaps they are truly native and only use OS libs)