The idea of Stack Exchange is to answer people's questions. Questions, funnily enough, are but a prerequisite to the all-powerful answers we're looking to collect. Because of that, there would be very little "actual value" to the actual purpose of the site coming directly from the bot. Value, sure, would come from people's answers to the bot's questions, but if nobody on Stack Exchange wanted those answers in the first place, that's not particularly useful.
On top of that philosophical barrier, there are some pretty significant (and in my opinion, less interesting, but still very relevant) practical ones, even on top of all of the natural language recognition and output that you'd have to worry about to make it even kind of useful.
- How can the bot answer clarification questions? "Show the the code you've tried?" "What jurisdiction are you in?"
- How can the bot decide which answer is best?
If your primary goal is driving more traffic to the sites, I think there are probably just way more efficient and effective ways to do it than through an automated process like that. There are millions of questions asked every day of search engines, and to sift through every single one (even aggregated and filtered by popularity), you're going to find a lot of pretty useless content.
Just as a personal example, I had to add a haircut appointment to my calendar last night, and I chose to use the automated assistant on my phone with a speech command to do it. My phone misunderstood my request for a calendar event, and sent me to the search page. The top four or five hits were Yahoo! Answers posts, the first of which being "I'm getting a haircut tomorrow!! What to do??"
I'm pretty sure we can do without a lot of the questions people ask on the internet, being on Stack Exchange sites. This bot would probably fall deserving of a question ban pretty quickly.
Long story short, to answer the question you asked, yes, I think this would be implementable, because I think virtually everything is implementable with enough lines of code. But I don't think it would be worth the effort.