You can if you want. The more live rock you have the faster the tank will cycle in my opinion and experience. But on the same note, you can add an ammonia source with only base rock and it will cycle as well. Live rock can introduce nice and not so nice hitchhikers and it will also, if you purchase a piece with coralline on it, bring that into your tank. The purple algae will not grow unless you bring it in somehow. You can also, after cycling, put in snails or other critters that have purple on their shells and that would work also.
180g Reef - 60g Rimless Reef -90G FOWLR- 125g Malawi Cichlids- 40b REEF- 34g Fresh Planted-working on- 20L FOWLR- working on
I have a mix of many different saltwater fish amongst my tanks, but I love my Tangs most of all.