No, it won't. It will run most mogul based 250 watt probe start bulbs including XM, Ushio and Hamilton
You need to use an HQI M80 ballast or an electroninc 250 watt ballast to power an HQI 250 watt bulb.
Between those two ballasts, I would recommend the 250 watt HQI 80 ballast. Electronic ballasts under drive HQI bulbs. You will get better bulb performance with an M80 HQI ballast.