No, a burn-out is no longer Awakened. A major event (on the scale of the Halley's Comet worldwide mana surge) would be required to 'reAwaken' their magic, as happened to the ex-mage rigger in 'The Burning Times'. A mage standing in a fovae might have Magic 0, but it is a temporary condition, imposed upon him; he is still a mage. A burnout has destroyed the last vestiges of his magic, and no matter how much karma he spends on trying to bind power foci, he won't be able to do a damn thing. It's the difference between an empty bucket (the mage drained of his power) and a bucket with holes all through it, including in the bottom (the burnout).
Sparks are those who are Awakened, but whose innate Talent is so narrow that they can do only one thing. 'The Aware' is one such 'spark', using Priority D, gaining a Magic rating of 3, and being able to use one rating 4 Magical skill, most typically Assensing since it dovetails with . others would be those unpublished ones who can only cast one individual (or one category) of spell, who can only defend against spells, who can conjure only one type of spirit (or, possibly, only one particular spirit, with restrictions on its return after being destroyed/banished equivalent to that of a free spirit's return), who can only banish spirits, who can only enchant one type of focus, or other similar 'one-shot wonder' sorts. A magic 1 spark will never (without GM's permission at expanding their ability range in steps, and in exchange for whole bucketloads of karma) be able to do more than that single thing - but that doesn't say they can't get extremely good at what they do.
Take the Aware spark as an example. This assensing wonder is already professional-grade at their own little narrow corner of Talent, and with a few add-ons from elsewhere (2 special attribute points and 2 skill points) and a proper build otherwise could very quickly fit into the slot of 'Knight Errant astral detective'. Add on a few years and more karma, and soon you have a Grade 4 Initiate with a Magic 10 and the ability to not only Mask, but pierce Masking, use Sensing to feel astral energies without even needing to shift their perceptions, and use Psychometry to gain information off objects. And nothing says they cannot bind weapon foci; if they went with some sort of melee combat skill, well - they might not be adepts or mages, but that experienced KE 'spook' with that old horn-handled knife on his belt could go one-on-one in a knife fight with some of the nastier gangers in the sprawl - and come out on top.
For those looking, the stuff quoted by Senko is Forbidden Arcana, p.102. The demographic sidebar giving the numbers layout is p.105.