No. In fact it is totally unheard of. No one fought with two swords in Classical Greece. I'm afraid I can't really spin this out to a longer answer - there simply is no evidence of anything like this.

Harmodios and Aristogeiton are no exception. In other depictions of their assassination of Hipparchos, they are shown holding a sword in one hand and its scabbard in the other (as you can clearly see in this rendering of a famous vase painting of the event). It was common practice in Ancient Greece for swords to be held by their scabbard rather than slung from the shoulder or belt, even in combat (usually the hand holding the scabbard would by protected by the shield).

As you point out, the surviving statue of Harmodios and Aristogeiton is not a Greek original, but a Roman marble copy. It seems quite possible that the people who made the copy misunderstood what the original statue actually showed. The stance of the two figures is quite natural and sensible if you assume that their off-hand is holding an empty scabbard rather than a second sword. They are shown in the act of killing; they have just drawn their swords.