Did Voldemort know the Vanishing Cabinet was in the same room as the diadem?
As TGnat’s answer and quotes show, the assumption in the question that Voldemort tasked Draco with using the Vanishing Cabinet is almost certainly incorrect. It was Draco’s own idea, and his own execution.
Voldemort himself was not—for whatever reason—involved in the events of that night when the Death Eaters were sneaked into the castle. He would, in other words, only have the reports of others (whether Draco himself or other Death Eaters) to rely upon.
Since Draco knew perfectly well what failure meant, it seems likely that he did not confide the details of his plan to anyone (we know for certain that he withheld it from Snape) until he had successfully repaired the Vanishing Cabinet and transported something to Borgin and Burkes and back again.
As it happens, we know with almost certainty that this happened almost immediately before Harry and Dumbledore left to go destroy the locket in the cave. In chapter 25, “The Seer Overheard” in Half-Blood Prince, we are first told that it is evening (my emphasis):
On one such evening, when Ginny had retired to the library and Harry was sitting beside the window in the common room, […] Hermione dropped into the seat between him and Ron with an unpleasantly purposeful look on her face.
During their conversation, Jimmy Peakes gives Harry a note from Dumbledore to come see him immediately. On his way there, Harry runs into Trelawney, who has just been forcibly thrown out from the Room of Hidden Things by someone male who was whooping with happiness. There’s a bit about Snape being the one who overheard half the original Prophecy, and then Harry goes to Dumbledore’s office, whence they set off for the cave at once.
This whooping, male Trelawney-ejector almost has to be Draco who has just managed to retrieve something from Borgin and Burkes—there would be no reason to include it in the story if it were anything else. Even Harry assumes this to be so in his conversation with Dumbledore before leaving for the cave. Assuming I am right that Draco told no one of his plan until he knew it would work, this means that Voldemort wasted no time in putting the plan into effect—it had been carried out mere hours after Draco sent word of it to him. The description and details of the plan were thus likely rushed through.
There is no evidence to suggest that Voldemort was ever told exactly where inside Hogwarts the newly-repaired Vanishing Cabinet was located. The plan was extremely simple: get Death Eaters to Borgin’s and Burke’s, have them go into the Vanishing Cabinet, and they will appear at Hogwarts, whence they will be free to wreak havoc and secure the way for Draco to kill Dumbledore.
In describing that plan to Voldemort on a tight schedule, there are many details that are more important than the precise location of the Vanishing Cabinet: where Dumbledore was, how to lure him back, who should play which role in wreaking havoc, where to lure Dumbledore to, etc. Even if the location of the Cabinet was mentioned in all this, it is not unlikely that it would be in more generic and practical terms, mentioning the location of the room (“once the Death Eaters are through, they’ll come out in a room on the seventh floor in the eastern tower”), rather than describing in detail what the actual room itself is, which is really quite irrelevant to the plan itself.
As it is we have no evidence to either prove or disprove that Voldemort knew the Vanishing Cabinet was in the Room of Requirements, but there’s at least a good case to be made that he didn’t.
Does it matter?
Quite apart from that, though, he was right: despite all the students who had been using the Room of Hidden Things over the years since he hid the diadem there, no one did know that that’s where it was. Even Harry, who had actually handled the diadem with his own two hands, had not recognised it and did not know where it was, despite the fact that he was actively searching for it.
There’s a good chance that, even if he realised that the Vanishing Cabinet was in the same room as the diadem, he would not be overly shaken by the fact. His method of security through obscurity was as good as it had ever been, and the fact that others had also found some use for the (enormous) room did not really change that. He alone did know where he had put the diadem, at the time.
And very importantly: he is trying to calm himself down by convincing himself of the unlikelihood of anyone knowing about any of the Horcruxes. He is enumerating and exaggerating reasons why no one could possibly know about them. He mentions the ring, the locket, and the diadem, and the other two are also exaggerated:
No one had ever known him to be related to the Gaunts, he had hidden the connection
One had only to do what Dumbledore did and look into his orphanage past to find out where the name Tom Marvolo Riddle came from; not too difficult to discover.
And how could the boy, or anybody else, know about the cave or penetrate its protection? The idea of the locket being stolen was absurd …
Both Regulus (with Kreacher’s help) and Dumbledore (with Harry’s) managed it, nonetheless. Again, his orphanage past held the clue.
Speaking logically, even Voldemort would probably have to admit that all three statements are not absolute. It would be theoretically possible to discover his connection to the Gaunts; there was at least one or two ways to come to know about the cave; and he couldn’t know for sure that others did not have as intimate knowledge of Hogwarts’ secrets as he did.
But Voldemort is not thinking logically at the moment: he is convincing himself, calming himself down, and using his exaggerated and arrogant sense of superiority as a tool to do so.