Imran bhai aap ki baat mein wazan he magar yahan issue yeh nahi he ke GS STOCK Battery ki life kitni he, going back to poiint which is, wheather GS can charge its "battery" with hid installed or not, and how much KMs it requires in day to be "enlightened" at night.
so my opinion is near to YES, because GS already keeps is H/L bulb always ON via battery when riding/driving at night, it does not give current throught magnet, and there is no "guidline" about bike to run it 50-60 km in day if you want to light ur bulb at night. So if it can light a 20-35 WATT bulb countinously, then it can probably light 55 WATT HID. (minor problem may occur with a very long drive at night, which can be resloved adding a few more Amperes).
that is because HID always need constant volts nearby 13.5 or 13, and it will start flickkering if going below than 12V, on 12 volts all your brake lights, idicators and even Horns and ordinary bulbs or other things will work fine