No, it doesn't modify
如果 or the phrase in between, and there's nothing to do with possessive constructs. I wouldn't even notice it when I speak, but when I think about it, I agree with hrzhu, that it can be loosely translated to
is the case, the actual words don't have explicit meaning here.
的话 provides a short pause, which gives the speaker a chance to actually think about the condition or assumption being said. It sometimes creates a tension, e.g.
如果我杀了你的话..., you can pause for many seconds here to frighten someone. Notice that
话 ends with the [a] vowel, so people tend to lengthen it when they don't know what to say, and need a sec to think, e.g.
So the idea is that with
如果 clause sounds more natural, because the condition or assumption being said does sometimes need a sec for you to pause and think. Without
的话, it sounds quite abrupt, although it does work if you leave it out, in most cases. Personally I call these constructs the lubricant of the language.