I'm currently downloading the iOS 7 update (7.01), but I'd like to wait a bit before installing it. After it finishes downloading, will it still stay in iTunes until I'm ready to install, or will it delete the file as soon as I shutdown? I used the 'Just Download' option, not 'Download and Install', so it shouldn't require me to install immediately after it downloads, but can I shut down so I can install later?
It will happily sit and wait for you to install it at your leisure. Apple even recently started background downloading this onto people's devices without them even requesting it, so that it is there when they want it. Suffice to say that some people did not appreciate this, especially as it takes up a lot of space just sitting there, which is the only downside of just downloading.