Rome at its apex had a population pushing at least 1 million people, that's in the city proper, not the surrounding country side. So Waterdeep having a similar population, which is what the current numbers purport, seems accurate. Plus Waterdeep does have sky scrapers, several of Waterdeep's walking statues have been hollowed out and converted into living space.
Waterdeep in DR 1372 had a population of roughly 130 thousand. Officially by DR 1485 it is over 2 million. That's not entirely unreasonable given that Waterdeep is very much an analogue of cities like London or New York. London's population around 1530 was 55 thousand, by 1605 estimates put it at 225 thousand. 1700ish it has doubled to between 550 thoussand and 600 thousand. By 1801 CE the offical London population was 939,300. So lets call that 1 million.
Waterdeep having a crazy high population isn't unreasonable, give that its a trade hub on the see one might compare it to New York which went from 60,515 in 1800 people to 3,437,202 people in 1900. That isn't counting the "outer boroughs" either that became part of the city in 1898. If include the outer boroughs in 1850 the population of New York was 696 thousand, but 1880 the population had tripled to over 1.9 million. That's only 30 years, so the idea that Waterdeep could see a population explosion isn't unreasonable.