I can see it from both perspectives here. The former obviously the one anyone would want to accept if they were in a situation where they were funded, but had no acceptance. The later, because it makes sense, why would a school take you if they rejected you just because you were funded?
I am hopeful that this won't be the case for me. That is, either I will be accepted and funded or rejected from both.
Throughout my undergrad training, I have been told - if you publish or receive a scholarship you will have an open door anywhere. I am starting to believe this is not true entirely.