It is possible to grow larger than the visa network with the current user rate in accordance to the time of existence.
I would say the bitcoin network definetly could get bigger then the visa network, and the time of existance is relativly small so it still has time to grow as well.
And if you look on blockchain.info and you see al the transactions already being made.
You realize this is really big already, the amount of people all over the world that are using it, we could form a Bitcoin country already!
No need to form such a country to establish our bitcoin. A lot of transactions are being used with blockchain but visa usage is high due to the universal acceptance. But if bitcoin gets universal acceptance, it will be controlled by someone which causes a backing in growth.