You will not get banned for using Blitz since it doesn't give you any unfair advantages in the game. You still have to play the games, just like everyone else.
In fact, many Rioters use Blitz too! We talk with Riot before developing any major features and make sure they are okay with what we are doing! Read more here.
The same goes for other games we plan to support in the future: any features we develop will be fully developer compliant.