I like the concept (But of course

):
The first Inuits are speculated to have arrived to Iceland in the 5th century ad. Little is known about them as Icelands volcanic earth has high acid and doesn´t preserve well. However some findings have illuminated us on how these people live.
In the first century the inuits continued their livestyle of fishing and stayed along the coastline, mostly in the south. In those days Iceland possessed big forests and the inuits embraced that, building huts out of wood and carving. Some artwork from that era were discovered in Thorsmork valley few decades ago. They are not very typical for the Dorset people in Greenland and Canada, and it seems that already then the inuits were starting to form a different culture more fitting to their surroundings.
In the beginning of the seventh century Irish people arrived to the island. The inuits and the ires which were known to the norse as papes were friendly. The Ires settled on the south coast of Iceland (
according to some OTL theories they did) and introduced to the inuits many new things.
The inuits did not settle like the Ires although they started trading with them. Some marriages between the two people did occur, after all both communities were very small and wanted to avoid inbreeding. The ires brought to Iceland cattle and grew wheat. They introduced to the inuits with some success christianity although they never managed to purge them of their pagan believes.
At the end of the ninth century the first norse arrived. At first they were friendly as well although conflict started later on when some inuits were enslaved. The Icelandic saga, Egil Saga, mentions how Egil´s father Grim manages to drive out of the fjord they settle, the local inuits. The norse often referred to them as trolls and looked down upon them. However just like with the irish interbreeding occurred and trade was vibrant.
By the year 1000 the irish had all either vanished or become part of the norse culture and the inuits had been driven from the best areas, to the northwest coast and south east coast. However as Njals saga tells us, the inuits had representation on the althingi when christianity was adopted in Iceland, and some heroes in the later written icelandic sagas are clearly of inuit origin.
The Icelandic inuit culture was unique and in modern Iceland there are still traces of it. The last hunters were still around in the 19th century on the northwest peninsula, but genome research has proved that as much as 30% of the icelandic genome is of inuit origin.
Note: OTL genome research proved Icelanders and greenlanders were related although it was less than 20%, around 50% of genes were of celtic origin, (or atleast believed to be), and some types in Icelandic have faces that remind one sometimes more of asians or nativeamerican than european, despite being white. (Take a look at Bjork for example).
well have to go.