Generally, no, it's not possible to put the TouchWiz UI on another phone that isn't made by Samsung. Because some pieces of hardware requires the hardware that a normal Samsung phone that naturally runs the TouchWiz UI has. That's also the precise reason why Samsung phones can't have HTC's Sense UI or LG's Optimus UI.
Even with rooting and if you actually have a dev that will try his best to put a majority of the features on the overlay, it would take up a lot of wasted time and effort because it would never be near completion and would have a lot of bugs and glitches that wouldn't be able to be fixed that easily. Hope this helped.
possible.....yes, practical no. simply because the developers that use these phone usually want to strip the "junk" out of the OS because it slows down the phone.
i have flashed ported touchwiz apps (s memo, calendar, launcher, s voice and maybe some others....been a while) on my galaxy nexus. they were cool for about....1 second. then i realized there were bugs and there were apps on the play store that would do the same thing with none of the bugs.