It seems to have been a matter of hit and miss as to what sculpture that Constantine had taken off from Greece to Constantinople survived until the sack of the city by the Crusaders in 1204 - and the same with all the books in the libraries that were in situ in the C4th. One lot seems to have gone up in smoke in a major fire in 466 around the statue-decorated Forum of Constantine (see my 'Chronology of the Byzantine Empire 330 - 1461', TM Venning, pub Macmillan / Palgrave 2006). Though the city was intact from outside attacks from 330 right through to 1204 (something of a record?) the physical appearance of it seems to have changed with a mixture of changing needs by the state and the public, eg fewer people using the public baths in a more family- and religion-centred public culture) and some crumbling buildings not renovated. So did the sculptures and other artwork get destroyed, broken up for reuse or sold off to private buyers when the buildings fell into disrepair or were remodelled?
To what extent did the Church's fulminations about 'immoral' nude statues or 'blasphemous and idolatrous' statues of gods cause damage or removal as respect for Romano-Greek pre-Christian visual as opposed to literary culture faded after c.400? Some of the main statues seem to have been intact as of 1204, as there is a record (possibly in Byz ex-minister Nicetas Choniates' contemporary history of the sack, translated in its 1984 Detroit Univ Press edition (trans Harry Margouliath) as 'O City of Constantinople', I think) of angry and superstitious crowds attacking the great statue of Athena taken from the Parthenon to Constantinople in 1204 as they had no idea of what it represented and thought it was 'beckoning Westwards' so inviting the Westerners to attack. The , damaged, victory column set up for the Greek victory over Persia at Plataea in 479 BC is still at the site of the Hippodrome racing-track , next to Hagia Sophia and the Palace; and probably other statues set up there were still there in 1453 when the Turks took over as there are Turkish miniatures of the remains of the Hippodrome in use for horse-racing or polo in the C16th. The famous group of 4 bronze horses ended up on St Mark's Cathedral in Venice - stolen like museum loot so in need of repatriation? The Fourth Crusade was one of the worst acts of cultural vandalism between the Late Roman temple-smashing in the Levant by militant monks in the 380s-390s and Henry VIII wrecking the abbeys and their libraries in England in 1536-40 (the dark side of 'Wolf Hall' politics).
Possibly if there had been no sack in 1204 more would have been left intact, though exposed to weather and neglect. And on the Alt Hist scenarios for the Fourth Crusade, there is a British twist to it all; the Crusader army would have been a lot smaller, and might not have broken into the city in the April 1204 assault (as opposed to managing to panic the useless Alexius III into fleeing in July 1203 so his nephew Alexius IV became their puppet-ruler) if the large Flanders contingent had not been there. The Flanders knights under Count Baldwin came on the Crusade partly due to the end of their earlier intended alliance with England and attack on King Philip Augustus of France in April 1199 after the sudden death of Richard 'the Lionheart' of England in a fluke lucky crossbow-shot at the siege of Chalus castle in Aquitaine. Had Baldwin's ally and patron Richard still been King in 1202-4 he was unlikely to have gone on the Crusade , or if he had done then ex-Crusader Richard would probably have gone too , to finish off his work in Palestine in 1190-2, and refused Venice's bribes/ blackmail to attack the Byzantines instead of heading for Jerusalem - and persuaded Baldwin to join him in Palestine. In that case, a smaller and poorer-led Crusader army doesn't take Constantinople, or if it does Baldwin and his hugely capable brother Henry are not there to lead the new Latin Empire. There is no 'Flanders/ Courtenay' dynasty ruling it as in OTL; it is more of a Venetian vassal city surrounded by hostile Greeks and Bulgarians. It collapses far quicker than in OTL, and the Nicaeans or the Angeli of Epirus regain it far earlier, c, 1220 or 1230, and a stronger Byz Empire is rebuilt - and may hold the Turks back??
'