As there are many examples in the various books of Ghouls having cybereyes and other cyber-augmentations i would say "it depends"
on what? the GM for one, but for another if its a Feral Ghoul, ya it would probably die. A ghoul that retains most of its "metahumanity"? no, as they could possibly have had a higher magic rating before the change and could therefore still have a decent magic rating afterwards.
Another example, is that when becoming a Ghoul you are GIVEN a magic rating regardless if you had one before, and your essence starts at 5 instead of 6 (body rejects cyberwear as well... eeewww) and as it states in the quote you gave you would loose your magical abilities (which means they basically just lose their Astral Perception (dual natured) abilites. That is through NORMAL means. But it says nothing about dying because of this loss of magic rating as mages and metasapients that burn out still can initiate and raise their attribute again if they have the potential for magic as you quoted from RF
Another Quote from RF p141 specifically relating to Infected:
All Strain II and Strain III Infected begin play with an Essence of 5 and a Magic of 1, unless they were magically active before their Infection. In this case, they begin with a Magic rating one less than their original Magic; the Essence lost to the disease takes the same toll on Magic as it would at any other time. They can increase their Magic attribute with Karma, like any other attribute, to a maximum of 5 + their initiate grade
It does go on to mention Strain I and the essence drain power and its ability to grant magical powers back that were lost because of their conversion to (in this case) vampires. but that may be beyond your question
Energy Drain, and its precursor in the CRB Essence Drain (both almost identical in wording) are a magical drain on your essence or magic or force etc. My interpretation would be that if you lose your above mentioned stats through these powers yes, you could potentially die.
As far as drakes go, (as you specifically called them out) the quote explicitly spells out what would happen, but yet it makes no reference to the drake dying. which again leads me to believe in my interpretation.
But to get back to your question, i think the answer goes along these lines:
Burning out occurs when your maximum magic reaches 0 and you no longer have the potential (even through initiation) to do anything magical at all anymore. All spells are gone, Adept powers, Critter Powers, etc. Until that point, you still have the potential for magic and have not "burnt the magic out of yourself", you are merely "locked out and cant find the key".
does that help?