The short answer is no.
According to Ohm’s law and the normal meaning of vacuum, a vacuum has zero charge-carriers and must act as an insulator. A voltage can be applied across a vacuum and there will not be any current because there are no flowing charges (since there aren’t any charges in the vacuum).
Vacuum-tubes, on the other hand, use hot metal surfaces to infuse electron clouds into a vacuum and then use high voltage (efields) to propel the electrons along. An electron-cloud can be created by applying voltage to the cloud and creating a charge-flow. We can also create electric currents in vacuum using ions (ions from red-hot chemical surface ions) and then driving the ion beams with high voltage.
However, it is important to remember that if the vacuum contains movable charges, it will not be a vacuum any more! The vacuum must first be contaminated with stuff or charged matter to become a conductor. Ideal vacuum is free from charged matter and has infinite resistance.
They shouldn’t be called “vacuum tubes”, but “electron cloud tubes” since they wouldn’t function if they were in a vacuum. The CRT tubes are correctly labeled as “cathode-ray” tubes. Cathode-ray used to be the old name for electron beam.
EXOTIC ANSWER This spontaneous “pair-production” is a dielectric break down, but not an gas-breakdown. It is a break down of the vacuum. See: Schwinger limit – Wikipedia
OT trivia: Electrons are not vacuum. Further proof: An individual discovered that an electron beam in a vacuum tube is sufficiently conductive to reflect radio waves. This was patented as a high speed scanning-mirror for microwaves and UHF. To build a video radar camera that can see the terrain, bounce your microwave beam at 60Hz off a rotating mirror, and then bounce it off an electron-beam at 15KHz in vacuum. An antenna is fed the raster-scanned beam. Then, use a broadband EM source to illuminate your landscape. Clothing and walls should appear invisible. You can find lost coins and gold rings in the sand.
ALSO, try… QUORA ANSWERS : W Beaty
 Heh, if an electron-cloud is a conductor, this requires that EACH SINGLE ELECTRON IS A CONDUCTOR! Apply a voltage, and if one electron is present, then the voltage produces a current. Once we realize that each electron is “a conductor,” then electrons behave like reflective metal balls, and all sorts of unusual effects suddenly make perfect sense.
Even rejected crackpotty claims can suddenly turn into predicted phenomena. Conductors, for example, are subject to inwards-directed pressure due to Casmir force (where two closely spaced conductive plates are pushed toward each other). A single electron must experience a titantic Casmir force, where reflected virtual photons push inwards from all directions. What happens when we put two electrons together? What happens if two electrons are placed close together? Will the area between them be shielded and electrostatic repulsion dominate the Casmir force? A little sphere of electrons could be used to shield the interior and crush it inwards through Casmir. Ken Shoulders believed so, and RP Feynman is said to have agreed. Shoulders patented a whole technology that involved “liquid droplets” of pure electron-clusters fired from sharp metal needle-tips. Shoulders discovered that bright, needle-shaped sparks coming from VDG machines weren’t sparks. Instead, they were glowing point-like objects moving at incredible speeds. Visually, it looked like a spark leaping. Shoulders invented “electron droplet” logic gates and circuitry. He also discovered x-ray point sources, death-ray weapons, and possibly the mysterious “glass-perforation” effect that we often encounter when using vacuum tubes with tens to kilovolts. A stream of electron-droplets can drill through bulk matter. If a sharp-edged metal structure is near a glass surface in vacuum and then exposed to some Kilovolts, the glass surface will mysteriously develop nano-perforations and start leaking air into vacuum.