I read up a little about this before replying. Some pretty good sites out there discuss this to some degree.
From what I gathered - I suppose it all depends on the species of live phytoplankton, how photosynthetic they are and their total numbers in the cycling tank.
If you dose too many - and they are alive and photosynthetic - they may consume much of the CO2 gas in solution and release O2 as well.
CO2 levels changing over a 24 hour light/dark scenerio could cause the pH to swing as it does in a mature tank.
pH swinging high can cause the ammonium ions to convert to the more toxic ammonia gas ion - and it may be more toxic to living things in the tank - including the critters hiding dorment in the live rock. Obviously it would depend whether or not this high pH occured, and how high.
The phytoplankton may use this ammonia and nitrite as food - but I'm not sure how they would affect the pH.
That's my only concern.
Otherwise it sounds like a cool experiment .... providing you are prepared for a good outcome or a poor one.
I think I would experiment on a smaller tank, and not my main display tank I was setting up.