Question: Some studies have shown that serif versus sans-serif on a computer display is not what affects readability and the practical differences between the two font styles are largely inconclusive.

I observed some designers prefer to use serif fonts only for titles or important elements and that make me ask: The font style on a CTA affect user's decisions?

Answer: 
I think you're talking about an [article by Alex Poole](http://alexpoole.info/blog/which-are-more-legible-serif-or-sans-serif-typefaces/). Anyhow, it basically says the same as you: in the battle of serif vs. sans-serif, there is not a decisive winner when it comes to legibility. They both have their pros and cons.

But size does matter in this case.  

Sans-serif is better when using a small font-size, because serif fonts tend to "smear".  

And sans-serif is also better in big font-size, think huge, like in advertisement billboards. Sans-serif is more legible from a distance.

So when your CTA button is small or huge, a sans-serif font would be the better choice from a usability perspective.

But other than that I think it's primarily an aesthetic choice. Does it fit the design?  

We could say that when it doesn't fit the design, the design will look incoherent and that might affect the opinion of the visitor about the company causing them to abandon the site. They could be of opinion the company might invest as less thought and effort in everything they do as they did on the design of their website.
I would avoid using serif for the call to actions unless you have a very good reason! Sans serif is easier to read, more modern. Serif is more likely to be used in a header, where it's larger text and ultimately more legible AND suits the design values of the brand (e.g. perhaps more traditional values)