I hope some of the following previous posts of mine might at least partly satisfy OP's curiosity:

• We often see the results of Viking/Scandinavian invasions/colonization on other lands like those of the modern British Isles, France, and Italy, but what effects did they have on the Scandinavian homeland?
• To what degree World the early church of Scandinavia be connected to the church of the continent and the papacy?
• The year is 1050 AD and I’m a decently well off farmer in central Sweden. While the king and many powerful lords have converted to Christianity I still hold on to the old gods. How open can I be about my faith, and how do I go about performing my rites? Can I in any way do it out in the open?

Would we have seen more centralized power structures in Scandinavia without the christianization of the region?

It would be not impossible to build such a temporal political dominion for non-Christian Scandinavian rulers, as was the case with King Gudfred (d. 810) of the Danes who fought against the Carolingian Franks and apparently extended his political influence up to the Oslo fjord in the beginning of the 9th century, but, as suggested in OP above, the missionaries, church organization, and the administrative literacy represented by the Christian clergy was indeed useful tools to establish more powerful 'overlordship' toward neighboring less powerful rulers as well as to build more stable rule in the kingdom.

• Famous 'Large Jelling Stone' (DR26) commemorates two or three deeds of King Harald Bluetooth (d. 987) in parallel, namely his political unification of the Danes and the Norwegians as well (just a overlordship?) and the conversion of the Danes. Adam of Bremen, a German chronicler, also often allude to the patronage/ delegation of missionaries in Scandinavia by powerful rulers of the Danes like Harald and Svend Estridsen (r. 1047-76).
• As I also mention a bit before in In the TV show Vikings, specifically S4 E18, the Northumbrian king brings his personal Bishop to battle with him. He is fully armored, and seemingly expects to partake in battle. Was this a common practice for rulers at the time? Or was it just an embellishment for entertainment purposes?, some Danish bishops in the 11th and 12th centuries often led or accompanied with the fleet, and a few of them were even known to have been a former naval commander or even a 'pirate'.