You'd still have to do something with it, either 'bury' it in the anoxic depths of the ocean and large bodies of fresh water, or bury it underground in either large pits or in caves/oil wells.
And you'd have to strip mine insane amounts of the necessary minerals that the algae needs, with regularity, to even approach sequestering a single gigaton a year, let alone the 40+ necessary to make a difference.
I'm all for figuring out carbon sequestration but I think YC's proposed paths for handling this in their recent call for startups looking into this are a bit silly. The flooding a significant portion of the Sahara for example will have extremely unpredictable weather implications which could be absolutel disastrous never mind you'd have to be mining minerals for use in the 'ponds' that is necessary for the life to grow in them which means you'd effectively need to fertilize a quarter plus of a continent with regularity every year for decades or even centuries. Even if you could fund that, it's not sustainable.
The real solution to carbon is immediate reduction of fossil fuel usage with a very short-term goal of nearly absolute cessation of greenhouse gas generation.
You then need to reforest 300 million acres of North America, restore countless miles of coastal kelp and seaweed, etc etc.
Even trying to replicate something like the Azolla event is unrealistic. If you take the 10 largest bodies of freshwater in the world and cover them entirely in Azolla, you are going to capture less than 10% of the carbon we are currently releasing each year and you won't even sequester all of that as to sequester it you have to sink the Azolla to an anoxic depth with every single generation of growth.
So, I doubt this algae would result in sequestering even a tenth of a percent of current carbon generation.