Is the square footage of the house all that you need to determine the size my air conditioner system should be?

For thumb rule you can use it to take approximate value but for exact calculations you need the following data

architectural layout

material of walls slabs

area location orientation

glass and occupant density

electrical equipments

lighting

fresh air requirements

But for quick check and reference we can use tonnage per area 

A good load calculation program takes into account window types, window orientation and window shading; insulation of ceiling, walls and floor; air leakage and many other factors such as the color of the roof and the number of occupants. Using the square footage of a home to size an air conditioner is outdated and will almost always yield an oversized system. Don’t use a contractor who wants to size your unit solely on the square footage of your house. Require a Manual J or equivalent analysis before purchasing.