Could Harry have used the Elder Wand to undo the damage to Hogwarts after the Battle of Hogwarts before he broke it in half and threw it away? In other words, would the Elder Wand have given Harry enough power to accomplish this task?
If Harry could have fixed Hogwarts with the Elder Wand isn’t clear.
There’s not enough information given to figure out if Harry could have repaired all the damage to Hogwarts himself if he used the Elder Wand. Harry wasn’t as skilled a wizard as Dumbledore, and though he knows the spell Reparo, it’s not clear how good he is at repairing things magically.
But - the Elder Wand likely would’ve been useful to fix Hogwarts.
However, though we don’t know if Harry could fix Hogwarts with the Elder Wand, the information given is enough to conclude that the Elder Wand would’ve been useful in fixing Hogwarts.
The Elder Wand could repair things that other wands couldn’t.
There’s conclusive proof that the Elder Wand can fix things that would otherwise be considered impossible to fix. When Harry shows his broken wand to Ollivander, a skilled and knowledgeable wandmaker, Ollivander tells him that a wand that damaged can’t be repaired by anything he knows.
“Ollivander held out a trembling hand and Harry placed the two barely connected halves into his palm. ‘Holly and phoenix feather,’ said Ollivander in a tremulous voice. ‘Eleven inches. Nice and supple.’
‘Yes,’ said Harry. ‘Can you –?’
‘No,’ whispered Ollivander. ‘I am sorry, very sorry, but a wand that has suffered this degree of damage cannot be repaired by any means that I know of.”
- Harry Potter and the Deathly Hallows, Chapter 24 (The Wandmaker)
Despite that, Harry is able to fix his broken wand by casting Reparo on it with the Elder Wand.
“He laid the broken wand upon the Headmaster’s desk, touched it with the very tip of the Elder Wand and said, ‘Reparo.’
As his wand resealed, red sparks flew out of its end. Harry knew that he had succeeded.”
- Harry Potter and the Deathly Hallows, Chapter 36 (The Flaw in the Plan)
Therefore, it would likely have been able to fix things at Hogwarts that would otherwise seem either difficult or impossible to repair.
Dumbledore used the Elder Wand to fix up the house Slughorn hid in.
While it’s not clear if Harry could have used it to completely fix Hogwarts himself, Elder Wand could certainly be used to repair things - Dumbledore uses it to fix the damage Slughorn caused when he was trying to make it look like Death Eaters had broken in.
“Would you like my assistance clearing up?’ asked Dumbledore politely.
‘Please,’ said the other.
They stood back to back, the tall thin wizard and the short round one, and waved their wands in one identical sweeping motion.
The furniture flew back to its original place; ornaments re-formed in midair; feathers zoomed into their cushions; torn books repaired themselves as they landed upon their shelves; oil lanterns soared on to side tables and reignited; a vast collection of splintered silver picture frames flew glittering across the room and alighted, whole and untarnished, upon a desk; rips, cracks and holes healed everywhere; and the walls wiped themselves clean.”
- Harry Potter and the Half-Blood Prince, Chapter 4 (Horace Slughorn)
This is another instance of things being repaired with the Elder Wand, though it’s not clear if using it fixed things better or more efficiently in that case.
We have already seen that the Hogwarts staff can undo spell effects on the castle with hardly a second thought. Flitwick undid the swamp spell made by the twins in a very brief time, and Snape is routinely repairing desks that are melted down by failed potion attempts in his class.
There may have been a few places where the curse had stuck (for lack of a better term) too firmly to the material of the castle for a simple Reparo to work. If the curse did not yield to their efforts to remove them, then it would have been a simple matter to remove the stone (or whatever) entirely and replace it with new material.
Taming the raging Fiendfyre in the Room of Requirement may have taken some doing. For the really tough cases they may have called on some professional curse-breakers (such as Charlie Weasley).
I don't see where the Elder Wand would have been necessary in all of this.
Powerful wizards and witches could have fixed the damage to Hogwarts without the Elder Wand; it just would have taken them awhile. The Elder Wand would probably have helped speed up the process.