I would say yes. Whether it is noticeable or not i cant guess. It is dead organic matter though and i have to think at least some will not be consumed. Assuming a reasonable dose it should be minimal.
I use live phyto(a lot) and it helps to control my nutrients but i did have to build up to a large dose. Initially i started too big and it was not being utilized fast enough and seemed to spike my nitrates. I would recommend live phyto for sure if that is an option for youm
It's really easy to culture. Just put a light over container with a bubbler. Add saltwater and your favorite living brand. Buy some fertilizer on ebay. . Add that. Room temp is fine. Every 10 days or so i just toss in fridge. When that batch is lower, cleaner the container, use a bit of it to start another. You can do this for a while. Kinda like culturing beer yeast starter cultures. If the culture poops out over time just get another bottle of your favorite as a starter.
I think corals eat dead or alive food, more to do with the size and coral in particular. I feed reefroids and live phyto. Reefroids (dead zooplankton) raises phosphate levels to about 0.13ppm in my aquarium whereas if I stop feeding it and just live phyto (and fish food), very quickly my phosphates drop to about 0.03ppm (took me a while to narrow down what was raising my phosphates, but eliminating one thing at a time did the trick)
I don't see any difference in corals either way and nuisance algae does not exist either way (except in refugium, but i am ok with that). Flowerpots (depending on what you have??), from what i understand and double check this, may like larger foods than Phyto instead (or as well) such zooplankton and finely chopped fish foods.