No, it has nothing to do with Pokemon bank.
Pokegen is essentially an illegal hacking device where you make Pokémon on a computer and put it into your game. This means you can create a good Pokemon, and make it better by giving it perfect IVs, an ability that it wouldn't usually have that would make it practically invincible ( e.g. speed boost & blaziken ( even though this was an event, but people who missed it make their own on pokegen ) and wonder guard sablye ) and making them shiny.
Pokegen created Pokemon are generally unsafe to your game and it is not advised to use pokegen at all. But people still do. You can usually recognise a pokegen Pokemon if its stats are impossibly high and it is level 100 and it is shiny.
Overall, pokegen is good if you want to make invincible Pokemon, but it is dangerous and illegal.
I am pretty sure I have got this right, but I might have got pokegen confused with something else.