Pseudo-Saturation, Massive Separation
"What happens if a skyscraper is built in a low-density zone, will it saturate the infrastructure?"
Let’s talk about the time during the construction of the skyscraper.
If the development of the skyscraper is complex enough to involve a massive coverage of on-ground messy work, not only that people wouldn’t want to stay there, the people that stay there would want to move out.
Just imagine a construction of the flyover in front of your house with unavoidable piling, hammering, metal cutting, trucks engine, horns, construction worker yelling that doesn’t stop during the daytime (night time as well for the road works).
When there is not “enough”(a relative idea of the number of people) population in a place, infrastructure won’t grow.
The government (typical kind) will not want to improve a place with a relatively less populated area than the city (observe rural areas of those developing countries).
And business prospect won’t come in - it is like you spend the same amount of money building a gym in a less populated area that has fewer people than in the city, regardless of not having competition.
The type of density and the type of building that you are building will also affect the chances the infrastructure being developed.
The government (in Malaysia, for example) would demand the developer to build certain related road access before a building development can be done as an express condition.
If a series of buildings comprise of office buildings and apartments that already have users from other places that want to move in to work and live, this would basically bring in the transient density that further activates the transportation system due to the need to travel.
But only when you have users that want to use the building. When you have enough people in one place, organically they would want a place to gather, eat, meet, get an education, work, worship, shop, and so on.
And development prospect might come in.
There are a lot of unoccupied tall buildings (apartment especially) in China being reported recently. Most of them come from a planned city that is quite the opposite to the idea of growth and more like an instigation (persuasion to convince someone that the buildings will eventually get used or get sold that didn’t work).
The pseudo-saturation became a massive separation.
(search: China ghost cities)
The key to saturating the infrastructure of a place becomes not by building a skyscraper, but building purpose of people using a place.