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.
I think 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. 如果他是GAY的话......他就不会喜欢你.
So the idea is that with 的话, the 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.
的话means in English. "If, say for example, blah blah blah..." – 杨以轩 Jan 09 '14 at 02:17如果...的话asif ... is the case. I'm not very sure, but I guess in most cases we can leave的话out. – hrzhu Jan 09 '14 at 04:32你想看的话.... It translates to "If you want to watch..." but literally is, what, "You-want-to-watch type of words"? My best guess for meaning is "(In regards to) the words/case of you wanting to watch..." Does that sound right? – musicnothing Jan 09 '14 at 18:20