I dunno about fish in a PC loop being plausible. The algae, food, waste, etc would wreak havoc in your loop/blocks. Saltwater also would be right out, conductivity and increased corrosion risk and all. Since you're in Australia, you have such beautiful reef denizens in your front yard, but the copper in the blocks kills marine invertebrates like corals, so no awesome saltwater tank.
But separate loops with a TEC heating the aquarium side and cooling the PC side might work. I would be concerned about the fish side getting too hot under prolonged load and too cold if you didn't turn your PC on often enough. You could balance that with a heater and a chiller on the aquarium side, but at that point there's no reason to thermally link the systems.
Yeah, it's too complicated and not worth the effort to combine them. A neat thought experiment though.
And on the topic of your desk:
Since you have a two piece desk surface, have you considered constructing your desk so that it can separate into two free-standing pieces for ease of moving?