Yes! When you use a page in a funnel, FunnelFlux will redirect the user to it and establish a "session" for that visitor.
You can see the VID value we pass into page URLs or that our JS gets and puts into the URL. With this ID we know exactly what funnel a user is in and what page they are on.
When they then click on an action link to go somewhere, we will send them to the correct page even if your current page is in many funnels (remember, we already know exactly where the user is).
You don't need to worry about this JS code causing problems. When a page is loaded with our JS on it, the code will first check for an existing visitor ID, which it might find in the URL directly, page referrer, or cookies, and it will continue to use this -- so it won't override the existing user data and cause problems.