and is there any benefit to running the refugium while cycling?
I would wait until after your first water change, where ammonia is 0, and you will be bringing the nitrates down from sky-high to pretty high. Then start up the refugium. I would even start the refugium before turning your display lights on, so that when the algae ultimately grows, it grows in the refugium, where it won't take hold and get nasty.
The algae will grow at the end of your cycle once the lights are on, the question is do you want the gross diatomes and green hair algae in the display tank, or back in the refugium, where you don't see it and don't care, and it's easier to remove the algae later in the game?