Question: I'm not sure if the death troopers speak entirely in what I assume is code or if it's just a very noticeable part of their communication and they do speak normally at times. 

Is there are a canon (and out of universe would be very interesting) reason for this?

Answer: 
Most special forces have their own special battle cant that is gibberish to anybody else hearing it.
Comms can be intercepted but decoding a specialised jargon or language would take insider knowledge.

Just take a look at [Enigma code](https://en.wikipedia.org/wiki/Enigma_machine) from WW2. Best codebreakers of the allies weren't able to crack it for a few years. Their only "breakthrough" came from acquiring an enigma decoder machine from a Nazi submarine.

Or take a look at [Navaho code talkers](http://www.californiaindianeducation.org/native_american_veterans/navajo_code_talkers.html), also from WW2... nobody but a Navaho would be able to understand even if the code could be intercepted over radio waves.
[![enter image description here](https://i.stack.imgur.com/qXE08.png)](https://i.stack.imgur.com/qXE08.png)

We do see this in many other universes too. Dan A. from W40K writes of battle-cant, battlecode etc.
They have encryption modules within their helmets that allow them to be able to understand what other Death Troopers are saying, but that prevents normal people without these encryption modules from being able to understand them. If you have read *Thrawn: Treason* you would know that Death Troopers are specially trained to be able to keep secrets even under pressure and torture, and this is why the encryption module was never stolen by Rebels, and why even Director Krennic can't understand them.