Telling the inhabitants of a coral that island that they're safe because sea level won't rise, is like a doctor telling a smoker, "stop worrying, you aren't going to die of lung cancer", while knowing full well that they're doomed to die from a coronary thrombosis. Ocean acidification (OA) and bleaching are killing coral and therefore—as a result of our unabated CO2 emissions —it's almost certain that all coral islands will disappear beneath the sea, whether sea levels rise or not.

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Bite notes: it's a common sceptic argument that sea level isn't rising and so low-lying islands are not at risk from climate change. But leaving aside sea level rise for the moment*, coral islands require living coral to enable them to maintain their height in the face of the constant erosion that occurs as a result of wave and storm action. Now ocean acidification (OA) and bleaching from warming seas are killing coral at an increasing rate, so in the long run it's almost certain that all coral islands will disappear beneath the sea as a result of global warming.

In summary; both rising sea levels and OA affect coral islands, but the rate of rising sea level mainly impacts the timeframe rather than the end result. 

*Oh, and by the way, sea levels are rising, and if they rise too fast even healthy coral will not be able to grow fast enough to keep the island above sea level. 

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Image source.