Not on my Samsung G S III it doesn't.
It has charts that lets a person input frequencies to convert etc, and displays frequencies used for various modes, but nothing I can tell that it's actually dynamically reading the cellphone state. But the info I do see is interesting as a reference as to what occupies the radio spectrum.
I don't get the displays that are pictured either, and there's no menu at the top right...
There is a paid version, but no info on what the differences are.
The app I do find helpful though is "Network Signal Info". It does give info on the cell connection, your wifi connection, both at once, and a phone hardware info page.
DAB listener 12/2003-11/2011 (DAB Off-Air since 11/2011)
HD radio Listener since 06/2010