As mentioned in the article, referring to "electricity" is kinf of vague. Ionized hydrogen floating about is a plasma; a collection of particle with a positive net charge. Therefore if some H+ ions move in a particular direction, that will be a flow of charge: an electric current.
Similarly H+ ions in aqueous solution can carry a current, as in electrolysis.
No, it doesn't have a positive net charge. In a plasma, the electrons are still part of the substance, but they are no longer bound to the nuclei, and are free to move about. Similar to current in an electrolyte, current in a plasma is the result of electrons moving one direction, while the nucleii are moving in the opposite direction.
Hydrogen gas is insulating matter. Ionized hydrogen is conductive matter.
Too bad we don't have metallic hydrogen. It would be a solid conductor, just like any other metal.
"Conductor" actually means "contains mobile charges." Conductor doesn't mean "a hollow pipe which electricity flows through." Conductors are more like long, narrow ponds. They're made of 'electric fluid,' so if we have a ring-shaped pond, we can push the water along so it starts moving in a complete circuit, like a drive-belt.
We have: On October 5th 2016, Ranga Dias and Isaac F. Silvera of Lyman Laboratory of Physics, Harvard University released the first experimental evidence that solid metallic hydrogen has been synthesized in the laboratory.
It took 495 GPa pressure to create. The sample is being held in the cryostat in liquid nitrogen.