Would time travel mean that parallel universes would be created off our linear time sequence to ensure the universe doesn't collapse itself because of significant events being drastically changed in the way it shapes the universe?

In theroy, yes. But time travel has yet to happen and thus, we dont know. I would assume that that if an alternate universe were NOT created, it would cause a rip in the fabic of time creating a worm hole and allowing all entitys to pass through simultaneously, and that would cause great stress on it, possibly causing it to rip large enough to encase the whole universe and it would implode.