Interesting. random thoughs; I would think that the stuff you're growing algae in might make a tea that would be nutrient rich. If you're pouring algae onto your soil, I imagine it would compete with your plants for nutrients and CO2. That is until it died, unless you over-water enough to kept it going. Like having moss on top of the soil, it would just suck up nutrients, not providing much benefit. I can't see where that would do any good.
Pouring dead algae onto your plants would probably be good, but you're pouring plant matter that has processed that nutrient rich tea to grow itself, consuming a lot of the nutrient to grow the plant matter including cellulose which isn't very easy to break back down into nutrient. My guess is you could do better using a kelp based fert, which is already been broken down to a degree. Algae is nothing more than a small single cell or multicellular plant that lives in water. If i tried it, I think i'd kill off the algae by boiling, then bubbling air through the solution for a day or two to let it degrade for a while. I could also see it rich in some beneficial chemicals/hormones that would promote/help aid photosynthesis. Sort of like pre-chewed nutrient for your ganj. Might do something good if the algae you use is right. I would think that single cell algae, or small fine algae like you probably have in your jugs, would be better than the fiberious matted type that you'd collect from a pond. Too much cellose development in that stuff. You probably want a higher ratio of green goodness from the inside of the cell. Bubbling air in your jugs will help grow the stuff faster and just like a hydro grow, you should make sure there's enough nutrient. Maybe go with a more rounded version of what you're using.
People have done weirder things and gotten surprising results. I wish you luck and hope you find something to accelerate our hobby.