I would make every effort to prevent it from growing in there. If you try to make it a harvestable nutrient sink, harvesting it will cause it to leach back toxins. Also, it WILL contaminate the main display, UV sterilizers are very puny against algae cells, and it would also cause fauna in the water returning from the fuge to be killed, which would be really lame.
Remember, algaes do things to the water to make the water suited for there own type of algae to thrive ONLY. This is very bad news if you arent trying to have a hair algae display tank.
There are simply better options for an algae nutrient export that work. I would kill off that hair algae patch pronto by anymeans nessicary.