Can Network Analyzer notify me when an unknown device joins my network?
To support this functionality, Network Analyzer would have to run in the background and scan the network all the time. First, this isn't possible because iOS limits what apps can do in the background (to save battery life). Second, even if it was possible it wouldn't be a good idea because performing the scan in the background would keep the CPU and wifi interface busy all the time which would drain the battery in a few hours.
In addition, it would work only when the phone is connected to your wifi and not when you leave your home with your phone which would make this feature rather useless.