It sounds like you're assuming both pieces are running on the same server, which may not be the case (and if you're bottlenecked on the database it probably shouldn't be, because you'd want to move that work off the struggling database server)
Assuming for the sake of argument that they are together, you're still saving stack memory for every thread that isn't created. In fact you could say it allows the CPU to be idle, by spending less time context switching. On top of that, async/await is a perfect fit for OS overlapped I/O mechanisms for similar reasons, namely not requiring a separate blocking thread for every pending I/O (see e.g. https://en.wikipedia.org/wiki/Overlapped_I/O, https://stackoverflow.com/a/5283082)
Assuming for the sake of argument that they are together, you're still saving stack memory for every thread that isn't created. In fact you could say it allows the CPU to be idle, by spending less time context switching. On top of that, async/await is a perfect fit for OS overlapped I/O mechanisms for similar reasons, namely not requiring a separate blocking thread for every pending I/O (see e.g. https://en.wikipedia.org/wiki/Overlapped_I/O, https://stackoverflow.com/a/5283082)