Will expensive strings make an acoustic guitar sound any better?
It is material and shape you need to pay attention to more than price.
This is specially going to concentrate on metal guitar strings. No, not the music genre. The material.
In the world of acoustic guitar strings, the material types you have generally available are bronze and phosphor bronze, and the shape can be either round or flat top. I'll cover the more exotic materials in a moment.
80/20 Bronze: "Loudest" string in most instances, meaning it projects the most. When you want an acoustic string that really rings out proper, you use bronze.
Phosphor Bronze: Not as "loud" as 80/20 bronze, but the overall sound is more balanced when strumming all the strings. If you encounter the situation when strumming where some strings are so much louder than the others that it presents a genuine problem, use a phosphor bronze string set.
Flat top: The D'Addario EFT16 set is an example of this. If the finger drag noise across strings really bothers you, then this is the set you want. It is phosphor bronze, so it will not project like 80/20 bronze does, but it will have a balanced sound without those annoying finger drag noises.
The more exotic stuff
Silk and steel: Several string companies make this. The string is soft both in feel and in tone. If your fingertips get wrecked easily from the regular options, you'll like these a lot. They are not expensive.
Coated strings: Elixir is the go-to brand for this stuff, and this is one where yes, you will spend more on these. Usually double that of a regular bronze set. Elixir does offer their acoustic coated strings in both bronze and phosphor bronze. These are worth the money for their longevity, especially if you don't play your acoustic guitar that often.
In the end...
You spend more money when you want the coated stuff that lasts an extra long time.
For just about everything else, you have to decide whether you want something that projects, something that's more balanced in tone, or something that feels more comfortable.
More often than not, it's the comfort factor that matters most. The more comfortable the feel when you play, the better you sound because you're not fighting with the instrument.
Go try a silk and steel set.