The One Ring and invisibility

[Findegil]

Well, I don't think that question is ultimatly answered by Tolkien in any of his writings. But he gave some hints. At least part of your question can be answered:

If Aragorn had put on the Ring, would he have become invisible?

Devinitley yes. We have the example of Isildur. In Unfinished Tales it is in detail told how he used the invisibility that the Ring granted to escape the Deaster of the Gladden Fields until he lost the ring in the river Anduin.
And from what we hear in the Silmarillion chapter Of the Rings of Power and the Thrid Age about the men that took the Nine it was not only the One Ring that made its manish wearer invisible.

What about Elrond, or Gandalf the Grey?

This is quiet another matter. We see Galadriel wearing her Ring and beeing visibile nonetheless and the same seems to be true for Elrond and Gandalf. Since we see the least mighty of the rings (the Nine) and the most mighty (the One) grant their manish wearer invisibility, it seems most probable to me that all the Rings of Power would have such an effect on man. But as we have seen not on Elves or Istari nor on Bombadil for that matter.

Why this is so is a question of pure speculation for which I will not go on. But I would like to remark, that even the Elves and Gandalf wearing their Rings did some tricy invisibility stuff with it, since no one could see the Rings on their fingers.

Respectfully
Findegil