I've read information about the possibility to use it to send Pokémon to the Bank and then Sun and Moon, but nothing about on wether I'd be able to do something like sending Pokémon from Yellow to Crystal and things of the sort.
The Virtual Console releases of the core series Generation II games are all able to use the Nintendo 3DS local wireless communication to trade and battle with each other, or trade with the Virtual Console Generation I games via Time Capsule, simulating the function of the Game Boy Game Link Cable. The process is done through the Virtual Console menu on the lower screen, with which players can establish connections through a hosting system. Additionally, these games can perform Mystery Gift with other Virtual Console copies of the Generation II games using the Nintendo 3DS infrared communication.
These releases are also compatible with the Poké Transporter, allowing one-way transfer of Pokémon in the player's first Box to Pokémon Bank, where the Pokémon can then be withdrawn by Pokémon Sun and Moon, Pokémon Ultra Sun and Ultra Moon or sent to Pokémon HOME.
Source
Yes, you can trade between Virtual Console games. No, you don't use Poke Transporter to do it. You can't put a Pokemon from a Virtual Console game into Pokemon Bank and put it into another Virtual Console game -- as the quote above shows, only Generation 7 games can withdraw Virtual Console Pokemon.
