Yes, it is.
I wouldn't say real, I would say more valuable. After all, most fiat money is digital, just like Bitcoin. The difference is that Bitcoin has increasing value due to scarcity and fiat decreasing value due to mass printing.
I wouldn't be surprised if some countries ban it, but I think it will happen to them like China when it refused to switch to the gold standard and continued with silver.
I would say it's more real than the money in the bank. I say this because we know that there is now (and for like almost always) more digital/fake/out of thin air money circulating than there is physical money, like notes, coins in the banks vaults. The easiest example I can say to express this is that if every client of a bank goes to their bank branches in the same day and they all ask to withdrawal their money, the bank simply won't have enough bills and coins to hand over to all their clients, because there is actually way more digital/fake money circulating than the one that physically exists (printed). And I think this is impossible with Bitcoin! I know there are also services creating virtual Bitcoin the same way banks do, but I'm not sure if the same situation could happen if we tried the same with Bitcoin!