Crushed coral as a buffer only works in fresh water tanks. In a salt water tank corals need higher levels of carbonates to form. So using coral won't raise Alk
Without getting too technical, alkalinity is the waters ability for water to maintain a stable pH or it's pH inertia. The higher the alkalinity is the more acid you would need to lower the pH.
Something like 97% of alkalinity is in the form of carbonates and bicarbonates. The rest is made up of other elements like magnesium etc.
So most pH buffers are simply made up of bicarbonates like sodium bicarbonate and carbonates. HOWEVER, sodium bicarbonate has a pH of about 8, so no matter how much you add, you'll never get to 8.3-8.4. Aquarium buffer also adds to natural alkalines so that it will raise alkalinity and pH up to around 8.4. The normal additional buffering agent is magnesium which we need anyhow.
Feel free to use pH buffers to raise your alkalinity because they are made up of the only thing that makes up 97% of alkalinity.
Also, baking soda can be used in a pinch to raise Alk
, but it will move your pH to about 8.0. Also it probably has a edible desiccant in it (borate if memory serves me correctly) to keep it free flowing which can build up in your aquarium and eventually cause a diatom outbreak.