I think the ambient background noise would be an excellent idea - the Close Combat series made very good use of that, as you could hear artillery and machine guns that sounded like they were in a nearby sector of the front. You would definitely want to make sound files specific to tilesets - would be somewhat disorienting to hear incessant mooing of cows in a city environment. But as an example, city combat would be made that much more authentic by the occasional police siren in the distance, trucks/trains/helicopters/jets passing, car alarms going off, muffled shouting, guns and/or death rays firing in the distance. Also consider day vs. night noises - i.e. crickets at night vs. birds in the daytime. It would go a very long way towards immersing you in the game world.
