I think the Elves (those who actually wore the Rings of power at the moment - and the Three and the Seven already had Elven owners) had indeed
heard Sauron's binding Ring-spell all the way from Orodruin. Just by Ring-magic. The Ruling Ring, when wielded by Sauron, seems to be strongly connected with the other 19 and could, it seems, be used for broadcasting. Sauron, however, hardly intended this to happen - his mistake.
Remember that when Frodo put the Ruling Ring on and
claimed it in Sammath Naur, Sauron was immediately aware of him. Perhaps partly it was due to the fact that Sauron at the moment had 12 rings in his possession?