Confirmed, I just did this for the first time earlier this week to buy a few tier points to get up to Gold. If you're logged into Finnair Plus, when you land on the Finnair Plus storefront it doesn't auto log you in, but if you click the login link you can use the existing Finnair Plus login in your browser and you don't need to enter any credentials. Other than you need to click the login link it worked seamlessly.