I don't know the superconductivity mechanism here (does anyone?), but IIRC Cooper pairs in BCS theory can be separated by much larger gaps than the transistors in a modern CPU — hundreds, rather than single-digits, of nanometers.
Might make fully-3D processors much more viable though, from lack of heat dissipation; and if it does, that in turn might be able to make up for a coarser resolution.
Also, the transistors themselves generate a lot of the heat... So you still have large amounts of heat to handle even if the interconnect traces are heatless.
undoubtably. We can't make things infinately fast. But being able to put the most powerful desktop processors and graphics cards we have today into a phone would definately be useful, not to mention laptops. It would also dramatically change how server farms work (their existance right now revolves around cooling, they could be so much more dense)