Admittedly I've never studied Trek 09 as thoroughly as the other films, but I don't recall seeing it either. Probably some are in holsters on people's belts during the evacuation scenes but I haven't step-framed every shot to check.
Communicators worn on the belts seem to be pretty standard on the Kelvin for some reason...
Yes the Tomorrow Show appearance is a must see for fans of TOS. Marred unfortunately by the presence of the curmudgeonly Harlan Ellison... :rolleyes
As to Kelvin Communicators, they are not QUITE the same prop from TOS... but they seem to be referencing the TOS comm flipgrid antenna in the construction of it. Different hole pattern though. And just like all the Trek 09 props, it looks rather whimsical and non functional... :unsure
That's somebody's Flickr picture from back when the film premiered, sorry if it is used without permission.
When I saw the interior of the Kelvin Comm I figured it was similar to the iPhone in that the whole interior surface is a control screen with changing images depending on mode and function.
The Nelson is a good refinement of the TOS phaser but my favorite will always be the version from ST3.