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: 
"Will serif or sans-serif fonts change the user decision/behavior on a call-to-action?"

The short answer is no. The serif may affect readability, and there is something to be said about aesthetics, but at the time of this post (2017) there is no conclusive evidence that a serif font influences user decisions. 

The rule of thumb is that sans-serif is more readable for small text and digital reading (think eBook). Serif fonts can help readability in "real world" tangible books (rumor has it these still exist in buildings called libraries). Most Call-to-Actions are some form of the button or smaller element on the page and thus do not contain large text, therefore sans-serif is probably the way to go.

However, largely differing font families (whether serif or not) can create different impressions on the user. Imagine if Amazon changed its font sitewide to Lucinda Cursive or something radical -- at the aggregate level, analytics would quickly show that user behavior is affected. 

Hope this helps to clarify.
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.