If a user swipes up in the app switcher then the OS will not launch the app unless explicitly told to do so by the user. So no, SLC will not be launching the app, nor will silent notifications. The only thing that will launch the app at that point is the user tapping the icon. The intention here is that the user has expressed their choice of not having that app running any more for any reason, so we honor that.
In this situation, there's really nothing that you can do. The next time the user launches the app you can let them know that some of the data may be missing, although you really cannot tell whether there's missing data or not (i.e. you might have been killed by the OS in the background and the user may not have moved thereby not triggering any SLC notifications). My suggestion would be to gather the data you can within the policies of the OS and if the user has manually killed the app then respect that wish and don't do anything.
iOS 7 also has a feature that will automatically start apps based on the times of day that you use them. So even if users are constantly dismissing apps from the multi-tasker (which I don't think will happen) the apps that are used the most will constantly be switched back on.
I doubt this statement is true. Some technical resources would be nice.