And based on physically seeing Robin dance with her dad at the wedding, the odds of Robin and Barney not going through with it have diminished. Obviously, there is still the possibility of that curveball, but the odds are extremely lowered.
Maybe it was because of the engagement episode, but I was really hoping that the reason for Robin's dad being all weird was going to ultimately be another one of Barney's long con's. In the end, we would find out that Barney had already gotten her dad's permission, and it was an elaborate setup. But, the ending they decided to go with was much better: Robin getting the first ever apology from her father in her entire life, and it was because Barney was able to get him to do it for her.