General relativity without quantum stuff admits closed timelike curves, but does not allow exploiting them due to the uniqueness of the metric. Quantum field theory on a CTC background very likely diverges in the way Hawking described. Actual quantum gravity might offer some hope, but in the weak field limit it is likely to match existing models, so the wormhole in question is very unlikely to be in this regime.
General relativity without quantum stuff admits closed timelike curves, but does not allow exploiting them due to the uniqueness of the metric. Quantum field theory on a CTC background very likely diverges in the way Hawking described. Actual quantum gravity might offer some hope, but in the weak field limit it is likely to match existing models, so the wormhole in question is very unlikely to be in this regime.