USB ports have a specific voltage and current ratings, see this entry on Wikipedia for the specifics. What this means, is that the maximum power that can delivered by a single USB port is capped.
One way to overcome this power cap is to use an external power adapters and many vendors opt for this solution, esp. for the larger capacity drives, however, this is solution is not very portable (you need to carry the power brick wherever you take the drive).
An alternative is to draw power from multiple USB ports, this effectively doubles your power-cap (atleast on paper). Some disks may even use the additional port to improve transfer rates, but I'm yet to come across any such disks.
Now as to what would happen if you use only a single connector is anybody's guess... the disk could operate just fine for some time and then tank, it might not spin up/be identified at all or it may malfunction in other ways. Generally, it would be a bad idea to use just one connector when two are provided.