Will the StrangerVille story-based gameplay appear for all save files?

For the most part the zombies stay contained in Strangerville. There are three stages of the story and in each stage more zombies appear. In Strangerville they will walk around all day.

There is an easily obtainable item that can make sims from any world into zombies. If these sims spawn in worlds other than Strangerville, and is between 1 a.m. and 4 a.m., then they will assume their possessed form.
So even if you infect all sims in your save, they will behave normally most of the time.

About the second question, the story is initiated by visiting a certain lot that the locals will point you towards and opening a door there. You do not need to be in the Strangerville Secret aspiration to do so. However, the "story" is not a series of quests or anything along those lines. All it does is move the town from one stage to the next. You can do your own thing in each stage, with no pressure to participate in the "story". It will patiently wait for when you are ready to proceed.