Actually, if Henry II died in 1157, then technically, Henry the Young King, having been born in 1155, would be next in line for the throne, by virtue of being the late king's eldest surviving son. However, succession rights were hardly set in stone and it is quite possible that the nobles might not want a child for a king and would pass him over for Henry II's younger brother, as you pointed out. Definitely some serious butterflies there.
I suppose it would depend on a number of factors. Would Eleanor of Aquitaine and even the Empress Matilda be able to drum up enough support for the boy? Possible, but not likely, I would think. The Empress was not well-liked in England, given her haughty behavior which had cost her the one chance she'd had to claim the throne in her own right years before. As for Eleanor, she was a foreigner and as tenacious as she was, most of the support that she might be able to count on was in Aquitaine, her own domains.