This question is kinda like "will Microsoft Office ever die out completely, and be replaced with an alternative office suite delivered via the Internet?"
In most literal terms, the answer has to be NO.
But, that's not to say that both things won't happen, and that there may well be a long period of overlap, which effectively makes the existence and rise of one basically unrelated to the death of the other. No, broadcast TV is going to die, because it will choose death over evolution, after a long and bloody protectionist fight.
Newspapers were heavily damaged financially by upstart free internet classifieds like craigslist. Broadcast TV has seen the rise not only of "internet tv", but also general non-video internet usage, as well as other video-centric entertainment sources like videogames as threats to viewership, and ultimately income.
Still, the greater threat isn't in "taking away marketshare/revenues", its in new solutions that create whole new markets that broadcast TV has a much harder time adapting to/incorporating. Take, say, CNN's use of Twitter(*) as an example. Craigslist isn't killing newspapers. A huge narrowing of the quality/performance gap between traditional newspapers and web journalism/blogging is what's killing newspapers.
In a similar manner, I expect that with TV, it's going to be less about "how long until they transition to Internet Broadcasting?", and much more about "how long until something new usurps Broadcast TV's central role in delivering news and entertainment?"
Not going to guess at an answer to that, but as I alluded to earlier, I fully expect that broadcast TV will not need to "fully die" first to allow such solutions to arise, and both solutions will coexist for so long it will be impractical or even disingenuous to call it a 'transition'. The US Post Office is still fending off email at a few cents per year, after all – but their organizational strengths in end to end delivery never led them to dream such a thing up, nor to imagine (or really even compete with) the likes of Fedex and UPS.
(* No really, take it. Take it far away, and burn it. At sea. A Viking's death for CNN's Twitter account. It's the only way.)