Thank you so much! So, it does look like it is possible, the way I read it. What is the source of this quote please? I wonder if I can get an official quote from somewhere...

I think the tricky part is whether TK will allow check in and/or generate boarding passes while we are still in the US (within 24 hours before the flight). This will probably put Finnair check in / boarding agents at more ease. Perhaps, boarding passes can be printed at the gate in HEL, but for check in in HEL one needs to clear passport control in HEL and that requires a visa...