It will spread by pieces getting dislodged, and reattaching somewhere else. So it's quite possible that it could migrate up to your display. The HA on the rocks you got is likely from a tank with excess nutrients like phosphates and nitrates which the new rock WILL leach into your water, which could cause your system to have high nutrients, and therefore become a good breeding ground for HA.
I would suggest you remove the rock from your sump, and put it into a Rubbermaid container with saltwater, a lid, a heater, and a good powerhead. Do weekly 100% waterchanges siphoning out all detritus. Keep it with good flow in the dark until all the HA is gone (this will probably take a couple months at least). Once the HA is visibly gone, test the water for phosphates and nitrates using good test kits like Elos or Salifert right before you do your weekly waterchange. Once nitrates and phosphates are both undetectable you can use the rock. You're looking at least 2-3 months. This process is called "cooking" live rock.