...But not with just the cell phone (stock software)?
If you hook it up to a tv you won't need any extra software. But in order to hook it up to the tv you need that adapter. If you're talking about on the phone itself, you can install a different launcher but that's the only way that'll happen.
I want a ROM that switches from the phone UI and dpi to the tablet UI and dpi when you connect the MHL adapter. The galaxy nexus has almost the same resolution as the current 10.1 inch tablets and that resolution would work just fine on a monitor with a keyboard and mouse. The only thing that's holding the nexus back is the size of the UI elements, which are way took big on a desktop monitor.