There is actually one instance of conversion by the sword which apparently took.It's that "apparently" which throws the whole equation.
1 Samuel 16: 7 -- But the LORD said unto Samuel, Look not on his countenance, or on the height of his stature; because I have refused him: for the LORD seeth not as man seeth; for man looketh on the outward appearance, but the LORD looketh on the heart.
In 878, King Alfred the Great, along with his Anglo-Saxon allies, successfully attacked the viking plunderers (read terrorists) and, after capturing their leaders caused them to be baptized and swear fealty to God. The vanquished kings and their people actually sought and recieved instruction in the faith and lived accordingly. Of course, in previous eras, one took oaths seriously, and followed whatever religion your leader or family head prescribed for you, an idea that is foreign to most today.
You can "follow the religion", but it doesn't, of itself, do you a darn bit of Salvific good.
For man looketh on the outward appearance, but the LORD looketh on the heart.
I'm not saying that there weren't "conversions"; I'm saying that any True Conversions which happened in the course of the above-mentioned affair, did not result from the efficacy of the sword.
John 6: 63, 65 -- It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.... And he said, Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.
You can't "make" a believer out of any man. You can only make him "follow the religion" at gunpoint -- if that. But it amounts to putting a sheepskin on a goat -- strap it on as tight as you like, it's still a goat. God converts whom He wants to convert; our duty is simply to Obey His commandments.
Romans 9: 15-16 -- For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
Or, since you brought up Vikings...
"The All-Father wove the skein of your life a long time ago. Go and hide in a hole if you wish; but you won't live one instant longer. Your fate is fixed. Fear profits a man nothing." -- Herger the Joyous, The Thirteenth Warrior
I don't know that the Christianity of these particular vikings is any more suspect than that of any other pre-reformation persons. They could only go on the knowledge given them, the same as others. The fruit seemed to be in changed lifestyles and support of the church.
Also, for whatever reason entered into - would it be safe to assume that some of Cornelius' household entered into covenant because their master said this was the way - a covenant was still made, and taken seriously, presumably, by both parties.