Is this theoretically possible?
No. Time travel is not possible. There is quite a bit of argument as to why it is impossible, but the simplest is that it hasn't happened. If time travel were possible, we'd see time travelers all over the place.
Of course, this forum is devoted to the development of fictional worlds. So our normal approach is to assume that your premise is possible in your fictional world. So here we'd start by assuming that in your world, paradoxes are not a problem for time travel. It just works. We could speculate as to why it works, but I don't know that it matters for this question.
Teaching advanced science
I think that you are overestimating the ability to teach advanced science. It's not as simple as just sending one person back. You'd have to send back an entire school system's complement of teachers.
Even if you only go a hundred years from 2015 to 1915, things changed a lot. In 1915, they still used slide rules. In 2015, we use handheld computers. What will we use in 2115? Maybe it's just more powerful computers. Or maybe it's something as different from an Android tablet as the tablet is from a slide rule. Do you know how to teach modern science with a slide rule? I certainly don't.
Moving the example to 4000/3000 doesn't fix this. It just hides it since we have no idea of what technology would be like in those years. For all we know, technology would regress during that period because civilization collapses in 3300.
Is this the best approach?
I'm not sure that lack of knowledge is the big reason for lack of progress. Consider what happened around the time of Christ. They stopped funding basic research. Changing that would have far more of an impact than sharing knowledge.
What would have happened if the Roman empire had become more democratic rather than more autocratic? Skip the Dark Ages entirely.
How I'd do it
Hand out time machines to everyone. People could do their research and then send the results back to themselves prior to when they started. That would save time individually and would speed research times going forward. Perhaps develop a short research cycle just to be able to reproduce the results. No need to go back hundreds of years -- days or months at a time is plenty.
Consider Edison's ten thousand ways not to make a light bulb. That took his people ten thousand attempts. What if they sent their research back. Skip the ten thousand attempts and go right to the working one.
Need to choose between two options? Pick one randomly, send the results back, pick the other, and send back both sets of results. Instant research! True A/B testing, as even death is reversible. Repeat the research with the same exact subjects but switch the choices. Or keep the choices and see if you get the same results.
Just the elimination of accidental deaths would speed up research. No car accidents or murders cutting promising careers short. Future Death division will take care of it (think about how Minority Report's Future Crime would work if they could predict all death).
Of course, the danger here is that someone will try a full on conspiracy to put themselves in power by changing the past. Of course, you have time travel too...