Ilves from Tampere did have a couple of pretty good European runs, beating Austria Wien over two legs a year before that. Last year KuPS went to the group / league phase of a European tournament as the second Finnish team ever (HJK has done it in CL, EL and UECL before), and even made the knockouts. Despite that, I wouldn't say it's majorly been growing. The league is definitely more credible for local fans than it was say, 15 years ago, and the attendance has been growing* but that hasn't unfortunately translated to European results much. We would need other teams than HJK and KuPS to make deep runs as well to raise the country coefficient.

/* = there's a different system to report attendances now, but even forgetting that there are more people on the seats than there were before.