Other than those who actively moved through the Shire, it doesn't seem that much anybody in Middle-earth had any significant awareness of their existence. The people of Rohan consider them a legend, the Ents don't even know they exist. I suspect that if some Elves didn't pass through the Shire en route to the Havens, and if the Dwarves did not travel through it, they'd have about as much awareness of them as the Ents or Rohirrim. Hobbits came to Sauron's attention only because of Gollum, and Gollum wasn't going to be much help locating the Shire, since he had never been there, and in his youth before the Ring, they lived in a different area. Moreover, there is in my mind a real question as to how much Sauron had truly "pulled himself together" by the late Third Age. Tolkien tells us he did have a body (not a beautiful one), and his mind was working well enough to focus on matters of war, but without the Ring, was he as strong or as sharp as he had been before?
Well, that's off the original topic. As to a link between the Shire's protection and Narya, I would agree with those who have said that Gandalf would need to reside there for Narya to be effective -- if it could have been effective at all. The power of the Three was in knowledge, understanding, and preservation, and unlike Lothlorien -- which Galadriel was attempting to preserve in a state akin to her memories of Valinor from her youth -- the Shire didn't require such an active intervention to keep it from the natural cycle of fading and dying in ME. The kind of preservation the Shire enjoyed was of a more mundane sort, which the Rangers provided. There did not appear to be anything extraordinary or "magical" in force. I believe that in the appendices, Tolkien says that before the end of the Third Age, it was suspected that two of the Three were in Rivendell and Lothlorien, and that many felt the third was probably with Cirdan at the Havens. I don't recall if he said it (the book is upstairs, and my knees don't care to make the climb at the moment
), but I presume that is because the Havens of the Third Age appear to be largely untroubled by forces of the Enemy. Whatever the case, there is no suspicion, even among those who know of its existence, that the Third is in the Shire. Perhaps Saruman, after he became aware of the fact that Gandalf had been given Narya, thought that he was using it to protect the Shire -- especially after he deduced that the One was there -- but if he did, Tolkien never mentions it.
Now, that went on longer than expected...
