Yes, the shells and reefs dissolve and the 'weeds' take over

Ocean 'acidification' causes concern but understanding of how it may affect marine ecosystems and organisms is 'limited' because almost all studies have been in vitro, short-term, rapid perturbation experiments on isolated elements of the ecosystem [1]. A newish paper [2] about localised acidification caused by undersea volcanic vents seems to confirm best guesses to date:

coralline algal biomass was significantly reduced and gastropod shells were dissolving... The species populating the vent sites...indicate that ocean acidification may benefit highly invasive non-native algal species.

Elsewhere [3], it's noted that avoiding environmental damage from ocean acidification requires reductions in carbon dioxide emissions regardless of climate change:

Projected changes in ocean carbonate chemistry should serve as a guideline for policy protocols that identify CO2 emission targets to reduce the effects of human-made ocean acidification. For example, to avoid a surface ocean pH decline by more than 0.2 units, total emission targets would have to range from ~700 Pg C over 200 years to ~1200 Pg C over 1000 years. Such scenarios would be difficult to achieve, however, because they require immediate reductions in global emissions.

Image: a 'rainbow of death' - explanation here.

Footnotes

1. But field studies from the Southern Ocean have already turned up evidence. See this episode of ABC's Catalyst.

2. 'Volcanic carbon dioxide vents show ecosystem effects of ocean acidification' DOI:10.1038/nature07051

3. Carbon Emissions and Acidification DOI: 10.1126/science.1159124, with news report here.