unless its a quantum thing where 1 bit can represent a series of quantum bits, but we are well far from that.

Isn't that a bit backwards? Qubits are taken from a continuous space, where as bits are taken from a discrete space. Thus you could claim that a single qubit can represent an infinite number of (classical) bits. But then, upon measurement, you can only really get 1 of them back. That's a bit of a problem since you can't clone quantum information, and you destroy it when you measure it. Then there is the idea of quantum teleportation (of quantum states/information), where you can transmit an unknown single copy of a qubit using 2 classical bits, and a shared EPR pair. You use up the EPR pair in the process, and destroy your copy of the qubit, but the two classical bits are enough to transmit the state to someone else to recreate the original qubit. The shared EPR pair is generally assumed to have been generated before hand, and each person gets one of the qubits from it.

But all that aside, the no cloning, and the measuring destroying the qubit would seem to imply you don't get any storage space improvements from quantum computers. Their real power is being able to set qubits in a superposition of classical states during a computation, and thus perform the computation for an exponential number of inputs. They're basically powerful computationally because of this extra interaction between qubits. But that also seems to be the problem with storing quantum information. As you may have heard, it's very difficult to build a quantum computer. Decoherence is a big problem. Any interaction with it's environment causes the qubit to be destroyed. It's hard to store a quantum state for any length of time, and from what I hear, if you can do it for about a second, you're doing pretty good. That would likely be quite the problem for a HDD like device.

And I'm of the view that a bit is simply a bit. It's a unit of information, mathematically defined to have 1 of 2 values. There is no way to map an arbitrary collection of 200GB*8 bits down to 200*8 bits, and then back again reliably so that any given input could be uniquely reconstructed. Trying to store the same amount of "information" in a smaller space is simply a change in storage media.

What would be the consequences?

I think this question is better if you drop the what if it's possible part, and replace if it, what if storage space suddenly got 1 billion times larger. That is, 200 GB can now be stored just as easily as 200 bytes can be.

If that was the case, I doubt there would be any real radical change or shift in society. Sure some people would claim it's a big thing, and it sort of would be. But do we really need that much harddrive space? Take the space you have now, and multiply it by 10 or 100. That should be more than enough to store pretty much anything you can think of for quite some time to come. The big drain on space, for home computers at least, is in media. If you have a lot of pictures, music, and movies, than you'll need lots of space. But even the first two don't seem to account for a enough to upgrade from current harddrives in most cases. And if they do, there's probably a big chance they're breaking the law.

So, I figure if we got that much more storage space, software/movie/music pirates would pirate more. There'd be increase demand for internet bandwidth, maybe more lag. It might be somewhat temporary, since an increase in pirating would probably cause a crackdown from law enforcement or the people behind them pushing it. If bandwidth suddenly went up a lot, ISPs would probably also crack down to save their bottom line. Or you might claim that bandwidth is largely already saturated for people who do that much pirating, that increased storage space wouldn't really affect their behavior. Although, with extra space, it would probably lead more people into the temptation to pirate stuff.

It'd probably be more useful for business to have more storage space. They often have legitimate reasons for having lots of storage. But then they can also usually afford to buy many harddrives to get the space they need. So I don't know if it'd be a big difference here. Maybe just a little more convenient. Perhaps some savings for them.