Theoretically yes. The question is if the low temperatures in space would allow the rod to heat up significantly, since the generated heat would be radiated out into the vast nothingness of space pretty quickly.
If there is temperature gradient in the copper rod, then the heat transfer will take place via conduction. It doesn't matter whether the rod is on earth or in space.
The articles say about conduction and convection in the medium (i.e. the atmosphere), not the copper rod or any other medium. Since there is no atmosphere in the space, hence no heat transfer in the space via conduction and convection. You gave an example of copper rod, so my answer was in reference to that.
If you are talking about the space in particular, so yes, heat transfer takes place only through radiation.
@AnanthDiwakar , yes it clarifies my doubt now. I understand that conduction and convection doesn't happen without a medium but if there is medium like copper rod then it would conduct.