But no, it would not and here's why - as Eobard Thawne said to Barry when Barry time traveled trying to stop the tsunami, time always has a way of bouncing back; of fixing itself. The weather wizard was brought down 24 hours earlier the second time around, only for the time gap to be filled in by the rogue's anarchy. Eobard was erased from existence, but they're using the time travel theory that is infinite earth's. Remember how Barry saw his reflection when running, and it was actually himself he saw from 24 hours later traveling through time? Even though Barry went back, the events that led to his time travel still existed in his reality (and Cisco's, but that's because he's Vibe), and two Barry's, for that brief moment, existed in the same timeline. Similar to the finale where three Barry's exist at one point in space-time. But, since Eddie killed himself, Eobard could have never been born, meaning everything that constitutes their realities no longer happened, meaning the very fabric of reality was destroying itself because it couldn't exist without Eobard and all the events he and his presence set in motion. To put it simply, think of it like this; you're adding 2+3+4, which gives you 9. 9 is your reality, but only because of the 2, 3 and 4 creating it. Take away any one of those numbers, the calculator will correct itself, giving you your new number (reality). This is the case of what's happening to the timeline we left off with on the Flash. Hope that helped!