the symptoms of the aap is very rough at cold idle....it will likely clear a bit after the engine warms up. most likely if it is leaking the carb will be very dirty (vacuum lines deteriorating from gas) and the engine will run very rich. alot of black smoke from exhaust. a simple test to check if aap is leaking is apply vacuum ( i did this with my mouth but if you don't like the taste of gasoline do not do it this way) when you apply vacuum ....if the diaphram is not leaking .....no gas will come from the vacuum hose. when you release vacuum a small amount of gas will shoot into the carb from the jet.

good luck
davef