When speaking about the Nazgûl The Silmarillion states:
And they became forever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows.
Does this mean that they are invisible to Sauron if he is not wearing or in possession of the Ruling Ring?
This is something that Tolkien never really explained in great detail.
We can gather from Gandalf's remarks in Rivendell that there are two worlds: the visible world and the invisible world:
You were in gravest peril while you wore the Ring, for then you were half in the wraith-world yourself, and they might have seized you. You could see them, and they could see you.
[...]
And here in Rivendell there live still some of his chief foes: the Elven-wise, lords of the Eldar from beyond the furthest seas. They do not fear the Ringwraiths, for those who have dwelt in the Blessed Realm live at once in both worlds, and against both the Seen and the Unseen they have great power.
The implication here is that mortal beings (and those who have never been to Valinor) live in the visible world, but don't have the ability to perceive what's happening in the invisible world.
Hence one of the effects of wearing a Ring of Power is to remove you from the visible world, but you still remain in the invisible world, and those who have access to the invisible world may still be able to perceive you.
Although Sauron never lived in Valinor (the Annals of Aman state that Melkor had already seduced him during the First Spring of Arda; i.e when the Valar lived on Almaren), we can deduce from the Akallabêth that the property Gandalf ascribes to living in Valinor above actually derives from living among the Valar and the Maiar; i.e it's not the physical location but rather living in the same place as where the Valar and the Maiar live that grants this property:
For it is not the land of Manwë that makes its people deathless, but the Deathless that dwell therein have hallowed the land.
Since Sauron did live among the Valar and Maiar, and was in fact a Maia himself, we can therefore deduce that Sauron does likewise "live at once in both worlds".
So far as a Ringwraith is concerned, it therefore seems evident that yes, Sauron would be able to perceive that they were not present in the visible world, but he would still be able to perceive them in the invisible world.
However, and as I said at the start, it is something that Tolkien never really wrote about in any great detail, and the best we can do is extrapolate from the fragments we have. We could go further than I have done here, but eventually we get to the stage where we're making statements that there is little or no authorial warrant for, and we have to stop.
Since the source of The One Ring's power is Sauron's own power, it would seem logical to think that Sauron could do at least some of the lesser things the ring grants a wearer on his own.
