This question makes several assumptions:
1) The "Many Worlds" Interpretation will have been proven through future observation
2) CTC's exist within the rotating event horizon of a Kerr black hole
3) Quantum fluctuations would influence the outcome of travel along a CTC
4) At some point in the future the first stable rotating black hole will be created in a lab
I'm envisioning a fictional scenario where a rotating black hole (albeit a "small" one that is not too massive-although I'm not sure what's considered small or large enough to make the CTC possible in the first place) has been created for the purpose of harnessing its rotational energy via the Penrose Process. Some mishap/plot device ensues, and a person passes through the rotating singularity, traveling along a CTC to find herself transported unwillingly several hours into the past, or in this case, a parallel world line.
So, to restate the question:
Would the creation of the CTC and subsequent travel to a parallel universe mean the effective waveform collapse of the previously inhabited universe via quantum probability? Or, put another way, assuming alternate timelines only exist as potential probabilities in the quantum foam, would the previously inhabited (present) reality exist independently of the new branch of spacetime or cease to exist?
(Please excuse any gaps in my understanding, not being a physicist this is all still very murky in my mind despite all the research. That's why I'm here.)