Correct me if I'm wrong but it looks like you set up this system with dry rock, dry sand and probably some bottled bacteria. I'd suggest adding some maricultured live rock, see
Aquabiomics article and add an urchin or two. When you do water changes you can also use
steel straws to remove some of the algae. And yes, algae can affect your corals, in several different ways, either directly shading and overgrowing them, causing anoxic zones around them with the DOC they release and by promoting pathogenic shifts in coral microbiomes with the DOC they release.
This is a lot to take in all at once so take your time studying it but here's some links if you want to understand the complexities of reef systems better:
"Coral Reefs in the Microbial Seas" This video compliments Rohwer's book of the same title (Paper back is ~$20, Kindle is ~$10), both deal with the conflicting roles of the different types of DOC in reef ecosystems. While there is overlap bewteen his book and the video both have information not covered by the other and together give a broader view of the complex relationships found in reef ecosystems
Changing Seas - Mysterious Microbes
Microbial view of Coral Decline
Nitrogen cycling in hte coral holobiont
BActeria and Sponges
Maintenance of Coral Reef Health (refferences at the end)
Optical Feedback Loop in Colorful Coral Bleaching
DNA Sequencing and the Reef Tank Microbiome
Richard Ross What's up with phosphate"