This question is intriguing because of the nature of the thermal cycles. This is the maximum theoretical efficiency of a thermal cycle (Carnot cycle), no ifs, ands, or buts about it.
You can obtain very low temperatures from space, because space is at a low temperature. You'll often hear the Cosmic Microwave Background (CMB) cited for this, but that's overly optimistic. A radiator could theoretically couple to that temperature, but in practice you would have to shield line-of-sight from every star in the sky. Practically, the averaged temperature of CMB + stars is a better lower bound, and you'll never get anywhere near to that.
If a blackbody was exposed to Earth's radiation and space in LEO, but was shielded from the sun, it could get to -30 degrees C. Obviously deep space probes don't have to worry about Earth radiation, and you could thinkably shield from that anyway.
We're left with the conclusion that T_C, in the Carnot limit, can be made very low. That suggests a very real possibility of a thermal cycle between the radiator and "room temperature". An engineer will hem and haw at the mention of this, but you could have a thermal cycle between those two things at 90% efficiency. I think we need to recognize that the answer to the question, as asked, is "yes".
Now, onto the qualifiers. There are a lot of penalties for ever setting up something like this.
- Space stations have to spend money on insulation to begin with, so you would increase that cost (dramatically), in order to avoid heat flow bypassing your radiator.
- What physical mechanism would you make this thermal cycle out of?
- The system would affect the energy balance of the station. It would have to be a part of the heat engineering from the ground up.
The only thing this really tells us is that it's not a serious near-term consideration. There are good reasons that we don't have a experience base for #2, for instance. There's a lot of work going on with recovery of waste heat, but often over small T differentials, but we don't often consider heat rejection at very low temperatures. It would only come into play for heat recovery systems in liquid nitrogen plants, for instance. If memory serves me correctly, I think thermoelectric systems depend on a very high temperature source. Everything is turned on its head when changing the temperature ranges like this. But there might be good options out there. This would be an interesting study area, because we just don't see those super low temperatures on Earth naturally. So it would rarely make sense to use it for heat rejection. Keep in mind, however, that good heat engines are not guaranteed. Thermal plants on Earth can often only produce 30-40% efficiency when the theoretical limit is 70% or so. That's because higher efficiency systems just won't scale up like we need. It's hard to say what efficiencies we could get.
But we wouldn't do it soon because space radiators are extremely large in size, modern designs require lots of mass, and insulation costs money too. The physical limit is area, from thermal radiation laws, but these are often made of metal sheets, or other things which are heavy. This is reasonable when you consider they'll have to hold in a fluid at pressure (and leaking is bad). The real limit is robustness for the space environment, ability to go up in a rocket, and the ability to unfurl itself into space. If you could spread out a much lighter sheet, it will cool much faster. But how could you recoup that coldness? And how is it going to hold up? In the distant future, space heat rejection systems have a lot of room to obtain very good performance through large, fragile systems in zero gravity. Same goes for insulation.
The heat balance with the station isn't completely self-defeating. This would only work if used with a station that was virtually perfectly insulated to begin with (long way off), but the "useful work" would be put back into the station. That creates an interesting situation where you get back a lot of the energy you consume. Low temperatures have economic value just as high temperatures do. But you'll have some other heat source (the sun, for instance) anyway, so any proposal for heat cycles coupling from station temperature to space also have to compete with coupling to the higher temperature. The ultimate design for heat movement between reservoirs would have to be considered in a holistic sense. But I could see how the OP's idea would make sense in a station powered by PV panels, for instance.