Yes definately. Very little is told about the events surrounding the forging of the Rings. We don't, for example, know who were the original Keepers of the Three Rings. It would be reasonable to suppose the Celebrimbor kept one for himself, but what of the other two?

With regard to the relationship between the Three Rings and the Nine and the Seven. It is worth noting that some have speculated that Sauron did not intend for Celebrimbor to make the Three Rings (they were made after he left Eregion). It is suggested that if Sauron had only to enslave the wearers of the Nine and the Seven he would have succeeded. But the unexpected addition of the Three to the 'net' meant it was not strong enough to hold all his victims and they broke free.

Either way, given the amount of time and effort Sauron put into the Rings of Power strategy, it was spectacularly unsuccesful.

Stephen Geard
Tasmania