Well, it would defeat the purpose of a "tech tree," although it might not be a bad idea. But I'm confused about the details. How would you get agriculture? Position a worker over a food resource? What if you wanted to get BW and do an early rush? How would these techs just "happen?"
Besides, having random things happen in any strategy game is bad. Just look at Civ 5.
Now, I don't know about ciV, and of course, things just happening randomly is kinda stupid.
As I said, I really haven't fleshed that idea out. It's just something that came to mind when playing civ (any of them). I don't even know if this idea is practical in any way and much less do I know how to teach the AI using it. I thought about it for the reason voyhkah mentioned: You cannot set out to invent something, it more or less happens. Of course there are technologies that were invented on purpose, like coal liquefaction. Many, however, were found by chance.
How you would get the techs in game, I don't really know. You'd need a ton of events (but they don't seem to happen very often even when iWeight is very high). Triggers could be having a resource on a city plot, having a unit standing on a resource, buildings, amount of great people (engineers raising the chance of discovering more technical techs, great merchants for socio-economic techs, prophets for religious etc.)
Or you could make the events (triggered by one/some/ all of the above) unlock certain technologies that you can then research. Having researched one would raise the chance of unlocking another tech that is directly linked to the one you just discovered.
As for the "how would I rush BW" question. Well, you wouldn't. You would go to war/ prepare for a war by building a lot of units and trigger the discovery of militaristic technologies.
However, I did not really plan to implement that (I myself am too bad a programmer to do that anyway). I just mentioned it because the OP seemed to be dissatisfied with the tech tree and I've been having this chimaera for a long time.