Considering the lack of action, or the very delayed manner in which we, the West, start to put up measures to prevent spread, I very highly doubt so.

Consider the incubation time of 5 days avg, 14 days max during which you're already infectious. Even if China had reacted quickly, not trying to cover it up, we still wouldn't have known about that for a while. Even without the Chinese new year, I'm pretty sure given how dense and large Chinese cities are, this would have spread eventually either way. And I doubt the rest of the world would have reacted any different in that alternate reality than now. We still have travel with China and Italy today. Why would that have been any different had China handled that differently? It would have been slower, but it would have spread to other countries, I have no doubt about that.