Yes you will have access since you're travelling internationally from Finland, so all sectors are considered international from Finland even though some of the flights only travel between cities in the US. This is important for not just lounge access, but also EU261, since if your flight to SEA gets delayed and you arrive at your destination 3 hours or more later than scheduled, Alaska would have to provide 600 Euros in compensation pursuant to EU261.

It should be noted (and you probably already know this) that in the US, you will clear immigration, pick up your bags from the carousel, re-check your bags for your connecting flight then re-clear security. In other words bags won't be checked through to your final destination.

I would encourage you to keep your boarding pass for the HEL-ORD flight, however, as lounge agents can and do get confused when presented with a domestic boarding pass even if the boarding pass has an annotation indicating it's part of an international flight (e.g. INTL annotation on United boarding passes). Showing the boarding pass from HEL and the boarding pass to SEA should be enough to get you into any OneWorld lounge at O'Hare.

-RooFlyer88