As far as I know, no. Not as well as an android phone, at least. The upside to the garmin etc are that they don't munch battery quite as fast and are better weatherproofed. This is solved by the backup battery and weatherproof case/a 'waterproof' phone.
Garmin etrex (more designed for hiking but useful for anything) will let you follow pre-planned routes and navigate to places ad-hoc but it's not as nice as Edge models for use while cycling.
So, before I go and get a new phone (I have a brick).... is there not a cycle-specific gizmo that does this too?