I do like your outside the box thinking. And as a bonus, ammonia is the most efficient refrigerant around, so you could use it in the A/C before it goes to the engine to be burned. But, I'm not sure of the chemistry on this one. Since NH3 is non-flammable, I'm assuming that your plan is to reform it into N2 and H2 between the tank and the engine. They naturally dissociate at 850F, so that might be a use for the waste heat of the engine. Although it would probably require the use of a suitable catalyst to bring that temp down a little bit. Running the fuel lines through/around the exhaust system sounds a bit complicated. On the downside, ammonia is VERY dangerous.
Anhydrous ammonia will combust, and there have been recip engines converted to run on anhydrous ammonia fuel. The problem is that ammonia has a very high ignition temperature, around 1200degF I believe. So it is difficult to use in CI engines without a pilot fuel.
Ammonia has average energy density, but it is easy to store since it becomes liquid at less than 10bar and RT. As for being hazardous, ammonia spills can be diluted with water. The only danger it presents is vapor toxicity to humans in higher concentrations. Anhydrous ammonia is also widely used as an agricultural fertilizer.