you always blow through the coil. A blower can blow air much
better than it can suck air. the blowers can develop static
pressure
to blow through a coil. they have made draw through coils, but they would have to be much larger to let the air flow through. this is why the furnaces and air handlers have different speeds, to match your ducts,and get the right pressures to move the amount of air you need for for your system. later paulbm

Actually I was taught the opposite. They suck better than they blow. That's why almost all gas packs have coil in return. Of course, heat exchangers on gas packs don't hold up and they wouldn't on a split system if coil was before the heat exchanger either.

The suction side of the typical squirrel cage blower is not nearly as good as the exhaust side.

The evaporator will not "block the heat flow from the furnace if it places after the furnace" it just introduces a small pressure drop. If it blocked it it would not matter what the order was anyway.

Placing A coils on top of gas heaters is pretty common.