It's generally considered inelegant but not nonsensical. There exist hidden-variable theories that reproduce all the normal predictions of quantum mechanics (including quantum computations), but they require non-local interactions. I think a restricted set of CTCs could mediate those interactions.
If we find quantum computers are no more powerful than classical ones, well then perhaps CTCs exist.
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Although what if quantum computing is actually a result of CTC under the space time fabric? (Probably a nonsensical proposition eh?)