WARNING Long rant incoming. Ahem. Every country is made up of waves of immigrants, not just the US. And Sweden isn't even traditionally homogenous, we have 5 recognized minorities and many more that are unrecognized. We have a rich culture of immigration and importing skilled workers. In the 1600's we imported Flemish smiths for our quarries, the most common inscription found in Sweden from viking times is "There is no god but Allah" - since we traded with the middle east and took their coins.
We took a french nobleman and made him our king, we've had Queen Kristina that converted to Catholicism, abdicated, and ran away to Rome, we have tonnes of loanwords from several languages since we've never been an isolationist country. We have a native people, the Sami people with their own language and rich traditions. We've treated them horribly in the past but we are trying to make that right. When Sweden realized what was going on during world war two we adopted an "We'll take them all" stance towards Jews - even though we were one of the first countries to start to sterilize people and had the institute of racial biology that was as horrible as you imagine. We have a lot of Romani people living in Sweden and a tonne of Swedish slang comes from their language. We were pretty shitty towards them in the past too, but we're working on it. We have groups of Finnish speaking Swedes since we used to rule Finland in a really shitty and colonial way - and there are still a ton of Swedish speaking Finns with their own beautiful dialect in finland. And the "homogenous culture" you think of (slightly Christian, quite secular, white and blond, using the Latin alphabet etc) isn't even that old. Until the 1200 or somewhere around there Sweden wasn't christian, we believed in our pagan gods. Christianity was brought to us by missionaries in the middle ages. We also used the rune alphabet for a long time and you can still find Christian rune carvings in really old churches. We still celebrate old pagan festivals like midsummer by erecting a giant fertility symbol and dancing around it. Until the 1800's we didn't even see ourselves as Swedes, we identified more with the surrounding villages than with the whole nation and a King that didn't care. It wasn't until a wave of nationalism swept the whole of Europe that we started seeing ourselves as Swedes. (It was this wave that led to the first world war) We used to own a large part of the Baltic, Finland bits of Germany etc. (http://en.wikipedia.org/wiki/Swedish_Empire) and until the beginning of the 1900's we also owned Norway. Sweden didn't take it's distinctive shape until the 20th century.
So, sorry no. No. If we didn't have immigration we wouldn't be the country we are today. Bonus; We had an almost literal pirate princess http://en.wikipedia.org/wiki/Princess_Cecilia_of_Sweden