Technically yes, but in practice the goal is to make the practical arrangements implementing of Article 5 security quarantees possible. There is not much use of NATO support, if alliance forces can’t operate in Finland in a practical way.
I am sure there are new operational agreements of similar nature will be made between Finland and Sweden as well as Finland and Estonia. That said, there is already a significant degree of defence cooperation between Finland and Sweden.
Finland is also already part of the british led JEF, and I would be surprised if the Nato framework would not change the nature of that cooperation.
Putin is probably miffed as the signing of a defence cooperation agreement between Finland and the US looms, which would bring US weapons to Finnish soil on a permanent basis. This is a step towards practical implementation of NATO defense collaboration.