[Evisse the Blue]

Man, that is one disgusting and freaky pic... Gollum was cuter...

but what if Frodo turned aside from his quest, and hid somewhere (like Gollum) long enough that the ring could take hold of him completely?

That couldn't have happened, from a historical point of view. Things were set in motion at that time, and Sauron was getting ready for to hunt high and low for that Ring while crushing Gondor and anyone who dared stand in his way in the process. Like Gandalf said, everything depended on speed. Considering that, Frodo could not have been in possession of the Ring for so long as to develop a Gollum-like appearance, Sauron's many spies would have caught up with him first. So such a thing is not possible even from a hypothetical point of view, it's totally irrelevant. They might as well have shown a picture with Frodo being tortured in the chambers of Barad-dur, that would have been much more likely to happen.