Not really. Firstly, it costs a lot more per square foot to build a high rise than a single family home. Secondly, it costs a lot more to maintain it (elevators need constant maintenance, you can't just run to Home Depot to get replacement drain parts, etc.).
And the infrastructure costs more to maintain -- running power to a high rise requires a lot of specialized commercial electric equipment that can handle the high loads and variability. Same with water -- you need special pumps and extra big boilers. Sure you can gain some efficiency by sharing those resources, but at the end of the day the costs per person are roughly the same.
The main impact comes from needing less transport of goods and people, which is an environmental plus, but not something priced into the cost of living.