Far as I know, breakdown in vacuum is much like breakdown in air; keep surfaces smooth rather than pointy; electric field causes atoms to eject and ionize (in a UHV environment, the metal surface itself provides material for the plasma discharge, but once it's going, it's pretty much the same idea).
Breakdown is typically several orders of magnitude better, so for example there are those friggin fancy vacuum variable caps, which might be as wide as your hand -- just to get enough creepage distance along the glass, really -- yet the internal electrodes are mm apart.
A coax conduit would be pretty cool, and bonus points if you make it out of niobium and supercool the whole thing -- then you can shove most any frequency down it, from DC to 100s of MHz. (Handy for collecting the radiation from one of those theoretical solar power satellite microwave downlink things?) 'Course, now we're talking really big bucks, for a list of reasons...
The biggest problem with a long vacuum conductor is the same seen in that TV transmitter video... the inner conductor needs support pegs on it periodically. Those have to withstand breakdown as well, and even in vacuum, creepage is a problem (consider the effect of adsorbed gas molecules). Maybe something ridged and spiraling would do the job?
One big downside is thermal conductivity: the center conductor is cooled almost entirely by radiation alone. Perhaps if the conductors are painted black on the facing surfaces, this wouldn't be too much of a problem, but it's a big hit on losses for sure (it's one thing to have losses, but with the temp rise, it's going to be that much worse, given the large tempco of copper).
It certainly needs to be constructed and sealed well, but for long distance, especially underwater transmission, that kind of goes without saying, anyway!
Tim