Dear Looking for Stats,
Short answers: Yes, and yes.
There's a Chance
That is, yes, you sometimes have a chance even after the "I just want to be friends" line is uttered, and yes, there is a chance to turn rejection into acceptance.
Good Friends Make Successful Couples
The happiest, most successful couples, of course, are good friends, so who better to get together than people who "want" to be friends.
I went out for a bit with a friend with whom I'd had that talk, so it is possible, but as with many (most?) cases, it depends on the individuals. You have to make the judgment, and talk about it with her. You have to determine that you're both interested (even if only in potential), then think about the pros and cons, advantages and pitfalls of hooking up.
Be Open and Honest
If you think the friendship can withstand whatever happens, and the potential benefits are worth it, go for it! All of this relates to turning rejection into acceptance, too talking about it openly and expressing your feelings honestly can go a long way.