The short version: no, but there is a useful perspective gained treating them as such.
Or, perhaps more controversially: not until recently.
That said, as was repeatedly emphasized to me in introductory linguistics courses, language is a fuzzier concept than our everyday use of it might suggest: dialects of "the same language" might not be mutually intelligible, as in the case of Chinese, or two countries might distinguish "their" languages from each others despite being perfectly able to carry on conversations.
Note: the remainder of this answer focuses on English, as this is the language I have firsthand experience of; it may generalize to other languages, however.
Specifically, the advent of the Internet and text communication has catalyzed the rate of change in written English, to the point where it may well be changing as rapidly (and diversely) as spoken English. Nevertheless, there is a fairly tight feedback loop between the two on account of the vast majority of English writers also being English speakers.
For example, consider the term "LOL". I think it is reasonable to say that this is not a term that would ever appear in spoken English without its textual counterpart; pre-Internet, written English was exclusively for formal or private use. I've witnessed the term make its way into spoken conversations, where it was pronounced either letter-by-letter or (slightly more recently) as a single syllable.
More recently still, the term has come back into written English as, variously, "lawl", "lulz", or "lel"; all express or refer to some form of amusement.
I should probably note here that this sort of written English is not what you would find in a dictionary - it is conversational, informal, and an artifact of typed (or texted) interface limitations.
While it is true that there are no "native" written language speakers, I wonder whether part of this absence might be due to the props required: the relative ease of learning a spoken or signed language means that the situation where a written language might become natively "spoken" never comes up (nor should it).
It should also be noted that written English has impacted spoken English before, and vice versa - just ask anyone who's failed a spelling bee. Acronyms such as "radar" and "laser" are inventions dependent on the alphabet - that is, the phonemes, so to speak, of written language (the technical term I believe is "graphemes").