The Legacy of the Levantine Norse- a Viking Jerusalem?

So, I was having my fun playing CKII as a Norse and doing a prepared invasion of Jerusalem that I turned into the Kingdom of Jerusalem. That got me thinking, what if it happened for real?
How and what the affect would have been, if the Vikings invaded and took the holy land?
I was thinking that maybe Christianity spread much faster in Europe, and so when the viking age starts, a significant portion of them are already christian. I believe that the most important factor for the viking age was over population, and thus still happen even if they are christians. Then some zealous norsman come up with the idea of gathering men to take Jerusalem in the name of Christ, and getting some land for himself along the way, with some rich plunder to boost! Is it possible? What do you think?
 
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