A Tesla uses around 300Wh per mile.
Coal power emits about two pounds of CO2 per kWh according to this page: http://www.eia.gov/tools/faqs/faq.cfm?id=74&t=11
2lbs/kWh * 0.3kWh/mile = 0.6lbs of CO2 per mile. However, that's before transmission losses and inefficiency in the charger and battery. Transmission is about 94% efficient (from http://www.eia.gov/tools/faqs/faq.cfm?id=105&t=3), charging is about 92% efficient, and the battery is about 90% efficient. That's about 78% efficiency in total, so divide that 0.6lbs by 0.78 to get 0.77lbs of CO2 per mile.
Burning gallon of gasoline emits about 20 pounds of CO2. Dividing by 0.77lbs of CO2 per mile gives us an equivalent of 26MPG, approximately.
Not spectacular, but not bad. The Model S is a big and powerful car, and similar gas cars have similar or worse efficiency. You'd be better off driving a Prius in this contrived situation, but then the "no real-world grid is 100% coal" thing comes in. For example, my local grid is about one-third coal, one-third natural gas, one-third nuclear. That cuts CO2 in about half compared to 100% coal, so now it's more like 52MPG. And coal's share is constantly sliding downwards, so over the lifetime of the car that number will improve.
I don't know as much about other emissions, but I'm confident the coal version will easily be better there. Big power plants are easier to run cleanly (they're easier to monitor, they don't care about weight nor much about space, and there's a single stationary point to install scrubbers, filters, and whatever else) and they tend to be far away from people.
Edit: I forgot to mention losses in the system from before the act of combustion. For a proper accounting, you need to account for emissions for the whole chain, from getting the stuff out of the ground to moving the car. Coal is much more efficient at getting out of the ground and into the combustion chamber, since it's already in burnable form, and then gets shipped in huge bulk by freight train. Efficiency losses there are single-digit percentages. Gasoline needs to be refined which alone takes something like 15% of the energy in the gasoline, plus transportation involves lots of small quantities being trucked all over the place. Total losses are about 20%.
I also want to say that I'm not really defending coal here, and I'd be quite happy if we could just stop burning it entirely. But the reality is that it's there, and it sucks, but even sucking as much as it does, it's still better than burning gas in hundreds of millions of little motors.