Officially. But in the interests of avoiding WWIII a weak west (led by Biden and his ilk) might try to find diplomatic solution.
Especially because "While part of the Kingdom of Norway since 1925, Svalbard is not part of geographical Norway; administratively, the archipelago is not part of any Norwegian county, but forms an unincorporated area. This means that it is administered directly by the Norwegian government through an appointed governor, and is a special jurisdiction subject to the Svalbard Treaty that is outside of the Schengen Area, the Nordic Passport Union, and the European Economic Area."
Notably, there is no passport control in Svalbard.