Just to avoid possible confusion in the photosynthesis equation you gave, CH
2O is formaldehyde, but it's a simple carbohydrate that works for a general explanation, but I am not sure that's what photosynthesis typically generates.
Dinoflagellates generally don't affect the alkalinity appreciably because they don't calcify in most case, as you stated. They will consume a bit temporarily if they take up carbonate or bicarbonate as a carbon source, but the alkalinity is released after the carbon is taken.
http://reefkeeping.com/issues/2006-10/rhf/index.php#6