Finnishness, an ethnic concept?

As we know, there is not that many foreigners in Finland, society is very homogeneous, and the country has a history of emigrants, not really immigrants.  Discussing these details with a couple of friends (a Finn by birth and a Finn by naturalisation) over a beer last Thursday, I started thinking that Finnishness is an ethnic, not only a cultural concept. 

This would be behind the perceived fact that an immigrant who comes here, no matter how well he/she (hän) adapts to the place, learns the language and adopts the culture will not be regarded as a Finn, even when holding a Finnish passport as he/she wouldn't "look like us".

If this idea happens to be right, it forecasts trouble for the integration of those immigrants that are already here and those that are coming, since the host society would not be ready for it.  Really wonder if that is the case.  Any opinions?

Not that nationality being a cultural concept is a guarantee of success.  Just ask the French.