Does completing an accelerated BSN program also make one an RN?

I would like to become a CRNA, and already have a BS. At this point, I only need to become an RN (as far as credentials are concerned). All RN programs I have seen so far are 2 years in length. Many acclerated BSN programs, on the other hand, are only 1 year in length. I want to become an RN as soon as possible, money more or less aside. My question is: If I were to complete an accelerated BSN program, would that also make me an RN, or would it simply give me a BS in nursing such that I would have to take further classes to become an RN? Another question I have is whether there is such a thing as an accelerated RN program, one that would take me 1 year or less and that is not an online program?

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