Did the fake Mad-Eye Moody ever use the Foe-Glass to learn Snape's true allegiance?

Question

This is a follow-up to my earlier question. That was about telling Voldemort about the Foe-Glass device, this one is about using the Foe Glass while at Hogwarts.

Barty Crouch Jr., while impersonating Alastor "Mad-Eye" Moody, had Moody's Foe-Glass in his office during Harry Potter's fourth year at Hogwarts. Near the end of the book, Goblet of Fire, the Foe Glass shows Albus Dumbledore, Minerva McGonagall, and Severus Snape just before they burst into the room to arrest Barty Crouch Jr.

This proves that all three were enemies of Crouch and therefore of the Death Eaters too. So Barty Jr. had an entire year to look through the Foe-Glass and know Snape was not really a Death Eater. It would be a major oversight for him to not check out friend and foe around Hogwarts.

Could he have used the Foe-Glass to learn Snape was not a true Death Eater?

If he did, he would have warned Voldemort and the other Death Eaters.

Edit: Not sure why this was flagged as a duplicate of my earlier question. As mentioned above, that question is "Did he tell Voldemort about the Foe-Glass?" which is different from this question "Did he use the Foe-Glass to learn Snape's allegiance?" It's quite possible for Barty Crouch Jr. to tell Voldemort about the Foe Glass and not learn about Snape's allegiance. It's also possible for him to learn about Snape's allegiance and not mention that or the use of the Foe-Glass to Voldemort. Neither condition implies the other. He could do both tell Voldy about the Foe-Glass and learn Snape's allegiance, or he could do neither.

Answer 1

Crouch probably assumed Snape was his enemy

From Barty Crouch Jr.'s perspective, Snape had been working with Dumbledore for 14 years. He had turned traitor against the Death Eaters and informed on them, and Dumbledore had publicly announced this:

Not yet!” cried Karkaroff, looking quite desperate. “Wait, I have more!”

Harry could see him sweating in the torchlight, his white skin contrasting strongly with the black of his hair and beard.

“Snape!” he shouted. “Severus Snape!”

“Snape has been cleared by this council,” said Crouch disdainfully. “He has been vouched for by Albus Dumbledore.”

“No!” shouted Karkaroff, straining at the chains that bound him to the chair. “I assure you! Severus Snape is a Death Eater!” Dumbledore had gotten to his feet.

“I have given evidence already on this matter,” he said calmly. “Severus Snape was indeed a Death Eater. However, he rejoined our side before Lord Voldemort’s downfall and turned spy for us, at great personal risk. He is now no more a Death Eater than I am.”

—Harry Potter and the Goblet of Fire

Crouch had little more reason to assume that Snape was in any way not his enemy than he had to believe that Dumbledore was not.

Also, as mentioned here, whether a Foe-Glass reflects someone may depend on more than their mere physical proximity.

The Foe-Glass would have posed a risk

Had Crouch been close enough to his enemies to see them reflected in the glass, they might have been able to see themselves reflected therein. And if, as associates of Moody, they knew anything about how the Foe-Glass worked, Crouch would be in real trouble. They would know that they were his enemies, which would mean that Moody was not who he claimed to be.

Answer 2

Crouch considered Snape an enemy anyway because in his eyes he was a traitor, no matter what Voldemort believed. He allowed Dumbledore to keep him out of prison, and as we know from Crouch/Moody attacking Draco, he held a similar grudge against the Malfoys. The Foe-Glass would show Snape as an enemy no matter his true allegiance.

Answer 3

No, Thats not how the Foe Glass works

The foe glass shows shadows unless you are personally in danger.

‘Oh, that’s my Foe-Glass. See them out there, skulking around? I’m not really in trouble until I see the whites of their eyes. That’s when I open my trunk.’

‘Stupefy!’ There was a blinding flash of red light, and with a great splintering and crashing, the door of Moody’s office was blasted apart – Moody was thrown backwards onto the office floor. Harry, still staring at the place where Moody’s face had been, saw Albus Dumbledore, Professor Snape and Professor McGonagall looking back at him out of the Foe-Glass. He looked around, and saw the three of them standing in the doorway, Dumbledore in front, his wand outstretched.

It took Dumbledore and crew to be actively intending to harm Moody/Crouch, and being within a few feet of him before you could see faces through the Foe Glass.

On top of that, being an enemy of Crouch != being an enemy of the Death Eaters.