Pondering this, I wonder what the point is of improving questions/answers that no one is reading. Is writing new answers to those questions going to make then suddenly start turning up in searches?
It occurs to me that as long as the version of this site on SE exists, it is what is going to show up in Google searches for any given topic. Not sure what you do about that. But that will mean that the only people who come here looking for answers will be people who know about this site and come here directly. What will they do then? Do a search here, or ask a new question? I suspect it will be the latter almost all of the time. (I suspect it was that way on SE as well, and that the only way people came there indirectly was via search.)
If people do search the site and find an old question that is relevant to them, then hopefully they will vote for the question and/or one or more answers, and that will the surface it as an active question. Or do votes not count in the activity of a question? And if they don't, maybe they should, at least for a while.
Anyway, I suspect that for a very long time to come, this site will sink or swim based on people asking new questions. Yes, that is more like a forum than a QA site, but my guess is that until a QA sites is rich enough and unique enough to rank on Google, that is how they are all going to work.
So, as far as traditional Q/A traffic is concerned, I don't think this proposal does anything useful, except entertain those of us who delight in answering question, whether the is anyone listening to the answers of not. (And I am one of those.)
The other model, in which this proposal would make more sense, is that of a band of regular site users who do not come to get specific questions answered, but who come either of a love of debating the craft, or as a way of getting an education on topics they might not have thought to ask, by looking at questions and answers that others have asked.
That might actually be what is happening here, particularly at this early stage, in which case, an algorithm that ensures that there are always fresh discussion topics, even if they are recycled ones, makes more sense, and would make sense as a permanent feature.
But in that case, it does not have to be randomly generated. In face, random generation would not produce an even distribution of resurfaced questions unless it ran for a very long time. So I would suggest a different model, that I suspect would be far easier to implement, and would ensure a more evenly distributed resurfacing of old questions:
Implement a list of "On this day in years past" questions. So, for instance, today it would list all the questions asked on Jan 10 in all the previous years in the dataset. That does the same job of resurfacing old questions.