I would imagine that OS X isn't broadcasting those messages via Wifi right now (although maybe you can configure it to do that...) so I think you'd need to make a small app for OS X which starts up during startup, connects to wifi (or whatever) and relays updates to the log file.
Then you'd need to actually make an iOS client application to receive those mirrored messages.
Can you get a dump to a text file, then echo the text file to an app. If you want real time display, you might look at a remote control package, but since the OS hasn't booted yet, you'd have to have something lower than the OS, like BIOS.