Growth of hard corals have two major pathways, growth of the soft tissue and growth of the hard calcium carbonate "skeleton". Both pathways demand energy input and building bricks from the water. This energy input will be present in two ways – by coral feeding and by photosynthesis. The energy input from the photosynthesis is normally the most important. The energy from this will together with nutrients in the water form the soft tissues and together with Ca and CO3/HCO3 (what we normally call alkalinity) it will form the hard CaCO3 that support the soft tissues of the stony corals. Because – normally – seawater have an “oversaturation” of calcium and in some way carbonates – the forming of CaCO3 normally needs lesser energy demand for growth compared with lower content of Ca and CO3/HCO3. Shortly – if your concentration of Ca and CO3/HCO3 get lower, the energy demand for forming CaCO3 will be higher and when all energy reserves is used – the forming (growth) of CaCO3 will get slower. If these changes happen slowly – I do think that there will be a point of concentrations, there the growth of CaCO3 will stop but that´s not connected with the surviving of the soft tissues that is more is in demand of nutrient and trace elements. The input of external food to your fish will probably give your corals soft tissue what they need for surviving.
However, if the alkalinity drops to much – you will see a pH drop that can affect all calcium carbonate structures in your aquarium but also stabilize the situation.
IMO if this happens slowly – as in your case – I think everything will stabilize in one or another concentration of Ca and CO3/HCO3 with very low growth of the corals – but I think they survive.
But when you will start to make your aquarium optimal again – do it slowly, very slowly.
Sincerely Lasse