They can still use the logo even if it is contested, unless some other business has already trademarked it, and can prove they have been using it for a longer period of time. If its contested, but not because its already trademarked, but because it is too generic, this also means anyone else can use it as well.
This is based on my experience, with a business that wasnt operating nationally. I got my tradename but not my trademark. If I wanted my tradename accross the whole USA I would have had to file for it in each of the 50 states.
At anyrate, not sure how the rules change on the larger national trademarking process.
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