Nope. That won't do anything but clear it up for 3 days, then it will come right back. You want your phosphate reading to be between .05-.03. Your reading of .50 to 1.0 is entirely to high, and this would lead to extensive algae and sponge issues.
Your going to need to run GFO or use a Lanthanum product.
I hear BRS has a good GFO to use.
Water changes won't get it out, not entirely. If you want to do water changes to get it out at that high of a range. Your new water needs to be coming through a RO/DO or store bought totally clean water. Then it would take you a ton of water changes to get it all out. Best to use GFO of Lanthanum.
I've had Big problems with hair algae in the past. But the way to over come it which I didn't know was my cause was the feeding ... IVe watched a video which probably most people do is wash your feeding . Take a small cup of tank water and put your food inside and let it defrost . Now skim it throw a fine fish net by pouring it throw from the cup to the fish net.. Now take a small cup of water from your tank to wash the phosphates and nitrates form the food and wash and pour it throw the net ... Now use that what is left in your food net to feed your tank... It has helped me for the last year with hair algae and I hope it will help you...