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I was told by a CSR, when my card was inactive due to non-use that I'd had to take a hard INQ just to be able to use it again. It wasn't closed yet. I said, I don't want to take a hard hit (or something like that) and she closed it! I said, "I didn't want it closed!" She said, "Oops! Well, if you want it, you can just apply again." I mentioned that I didn't want a new tradeline, and she said that there wouldn't be.
But, after she closed my account, I didn't have a lot of faith that she knew what she was talking about. Just call and ask them. Then, maybe call again just to make sure that you get the same answer twice.