Not quite as dramatic as your story, but I certainly say Yes to the question as put in the subject. My DSnow6 was a late talker, though, so it's hard to be certain how much he was reading before he could talk. Certainly some - when he was 17 months we had a weird experience where it seemed certain he'd read "DVD" on a promotional leaflet that had no picture of a DVD or anything else that seemed like a clue (he was mad about watching DVDs, and got very excited, although the DVD this was an ad for was an adult one with no attractive picture or anything!) I remember a discussion with DH about whether he'd only be able to read it in that particular font (the one associated with the trademark), whether he was likely to be able to recognise any other words, and how we could possibly tell given that he wasn't talking! I handwrote DVD and his (IRL!) name and a couple of other words on pieces of paper, and asked him which word said DVD, and which word said his name. In both cases he pointed out the right word without hesitation, and made what seemed to be an attempt to say the word. It just didn't seem to be right to be testing how much my pre-verbal 17mo could read, though, so I didn't investigate further. (I sort of wish I had, although I'm pretty sure I made the right call at the time.)
A few months later when he did start to talk, many of his first "words" were letters of the alphabet (many others were numbers). Certainly before he was two he knew all his letters by sound and by name, from Starfall (I remember joking that maybe he was going to send us email in full sentences before he talked in full sentences).
I'm not honestly sure how his reading developed in the following year - he used to recite his books, with or without the book in front of him, and I didn't want to quiz him, so it was hard to tell. He was 2y10m when I first saw (happened to see?) him pick up a book he'd never seen before and read it through. Around then he was getting obviously frustrated trying to read hard things, so I started buying reading scheme books and he sped through them. He started school at 4y10m reading chapter books and now he can read anything he wants to. However, true to the idea that early reading actually predicts mathematical ability better than literary ability, it's now in maths that he's most ahead (using a mixture of 6th-8th grade material now in what would be 1st grade in US terms).
Have fun!
